MathProblemsBank Math Problems Bank
  • Home
  • Forum
  • About Us
  • Contact Us
  • Login
  • Register
  • language
 MathProblemsBank banner

MathProblemsBank banner

Math Problems and solutions

Mathematics sections
  • Algebra
    • Vector Algebra
    • Determinant calculation
    • Permutation group
    • Matrix transformations
    • Linear transformations
    • Quadratic forms
    • Fields, Groups, Rings
    • Systems of algebraic equations
    • Linear spaces
    • Polynomials
    • Tensor calculus
    • Vector analysis
  • Analytic geometry
    • Curves of the 2-nd order
    • Surfaces of the 2-nd order
    • Lines on a plane
    • Line and plane in space
    • Tangents and normals
  • Complex analysis
    • Operations with complex numbers
    • Singular points and residues
    • Integral of a complex variable
    • Laplace transform
    • Conformal mappings
    • Analytic functions
    • Series with complex terms
    • Calculating integrals of a real variable using residues
  • Differential equations
    • Ordinary differential equations
      • First order differential equations
      • Second order differential equations
      • Higher order differential equations
      • Geometric and physical applications
    • Systems of ordinary differential equations
    • Stability
      • Stability of the equations
      • Stability of the systems of equations
    • Operating method
      • Differential equations
      • Systems of differential equations
  • Differential geometry
  • Discret mathematics
    • Boolean algebra
    • Set theory
    • Combinatorics
    • Graph theory
    • Binary relations
    • Propositional algebra
      • Propositional calculus
      • Sequent calculus
    • Predicate calculus
    • Theory of algorithms and formal languages
    • Automata theory
    • Recursive functions
  • Functional analysis
    • Metric spaces
      • Properties of metric spaces
      • Orthogonal systems
      • Convergence in metric spaces
    • Normed spaces
      • Properties of normed spaces
      • Convergence in normed spaces
    • Measure theory
      • Lebesgue measure and integration
      • Measurable functions and sets
      • Convergence (in measure, almost everywhere)
    • Compactness
    • Linear operators
    • Integral equations
    • Properties of sets
    • Generalized derivatives
    • Riemann-Stieltjes integral
  • Geometry
    • Planimetry
      • Transformations on the plane
      • Construction problems
      • Complex numbers in geometry
      • Various problems on the plane
      • Locus of points
    • Stereometry
      • Construction of sections
      • Various problems in the space
    • Affine transformations
  • Mathematical analysis
    • Gradient and directional derivative
    • Graphing functions using derivatives
    • Plotting functions
    • Fourier series
      • Trigonometric Fourier series
      • Fourier integral
    • Number series
    • Function extrema
    • Power series
    • Function properties
    • Derivatives and differentials
    • Functional sequences and series
    • Calculation of limits
    • Asymptotic analysis
  • Mathematical methods and models in economics
  • Mathematical physics
    • First order partial differential equations
    • Second order partial differential equations
      • d'Alembert method
      • Fourier method
      • With constant coefficients
      • With variable coefficients
      • Mixed problems
    • Convolution of functions
    • Nonlinear equations
    • Sturm-Liouville problem
    • Systems of equations in partial derivatives of the first order
  • Mathematical statistics
  • Numerical methods
    • Golden section search method
    • Least square method
    • Sweep method
    • Simple-Iteration method
    • Approximate calculation of integrals
    • Approximate solution of differential equations
    • Approximate numbers
    • Function Interpolation
    • Approximate solution of algebraic equations
  • Olympiad problems
    • Olympic geometry
    • Number theory
    • Olympic algebra
    • Various Olympiad problems
    • Inequalities
      • Algebraic
      • Geometric
    • Higher mathematics
  • Probability theory
    • One dimensional random variables and their characteristics
    • Theory of random processes
    • Markov chains
    • Queuing systems
    • Two-dimensional random variables and their characteristics
    • Definition and properties of probability
    • Limit theorems
  • Real integrals
    • Integrals of functions of a single variable
      • Indefinite integrals
      • Definite Integrals
      • Improper integrals
    • Double integrals
    • Triple integrals
    • The area of a region
    • Volume of a solid
    • Volume of a solid of revolution
    • Flux of the vector field
    • Surface integrals
    • Curvilinear integrals
    • Potential and solenoidal fields
    • Vector field circulation
    • Integrals depending on a parameter
  • Topology
  • USE problems
  • Variational calculus
Problem list Free problems

Attention! If a subsection is selected, then the search will be performed in it!

Problem: Find the solution of the Cauchy problem for the differential equation: \[ 4 y^{\prime \prime}+y=3 \cos x, \quad y(0)=-3, \quad y^{\prime}(0)=\frac{1}{2} . \] clip2net.com

8.1.2.88 Second order differential equations

1.8 $

Problem: Find the general solution of the differential equation: \[ y^{\prime \prime}+4 y^{\prime}+4 y=(2 x+3) \sin x . \] clip2net.com

8.1.2.94 Second order differential equations

1.54 $

Problem: Find the particular solution of the differential equation when \( f(x) \) is given: \[ y^{\prime \prime}+y=f(x) \text {. } \] clip2net.com

8.1.2.98 Second order differential equations

2.57 $

Problem: Solve the differential equation: \[ x^{2} y y^{\prime \prime}=\left(y-x y^{\prime}\right)^{2} \text {. } \] clip2net.com

8.1.2.1 Second order differential equations

1.8 $

Problem: Find the particular solution of the second order differential equation, satisfying the given initial conditions: \[ y^{\prime \prime}-3 y^{\prime}+2 y=2 \sin x, \quad y(0)=1, \quad y^{\prime}(0)=1 . \] clip2net.com

8.1.2.2 Second order differential equations

1.54 $

Problem: Find the general solution of the differential equation in parametric form: \[ \left(x+2 y^{\prime}\right) y^{\prime \prime}=1 \text {. } \]

8.1.2.9 Second order differential equations

1.28 $

Problem: Find the general solution of the differential equation in parametric form: \[ \left(y^{\prime \prime}\right)^{2}-2 y^{\prime} \cdot y^{\prime \prime}+3=0 . \] clip2net.com

8.1.2.11 Second order differential equations

1.8 $

Problem: Find the general solution of the differential equation in parametric form: \[ \left(2+y^{\prime}\right) e^{y^{\prime}} \cdot y^{\prime \prime}=1 . \] clip2net.com

8.1.2.13 Second order differential equations

1.28 $

Problem: Find the general solution of the differential equation in parametric form: \[ \left(3 y-2 y^{\prime}\right) y^{\prime \prime}-\left(y^{\prime}\right)^{2}=0 \text {. } \] clip2net.com

8.1.2.14 Second order differential equations

1.54 $

Problem: Find the general solution of the equation \( x y^{\prime \prime}+ \) \( +2 y^{\prime}+x y=0 \), if the function \( (\sin x) / x \) is its particular solution. clip2net.com

8.1.2.15 Second order differential equations

2.06 $

Problem: Find the general solution of the equation (1\( \left.-x^{2}\right) y^{\prime \prime}-2 x y^{\prime}+2 y=0 \), if the function \( x \) is its particular solution. clip2net.com

8.1.2.16 Second order differential equations

2.06 $

Problem: Solve the following equation using the method of variation of arbitrary constant: \[ y^{\prime \prime}+4 y=\frac{1}{\sin ^{2} x} \text {. } \]

8.1.2.17 Second order differential equations

1.8 $

Problem: Solve the following equation by the method of variation of arbitrary constant: \[ y^{\prime \prime}+4 y^{\prime}+4 y=e^{-2 x} \ln x \text {. } \]

8.1.2.20 Second order differential equations

1.8 $

Problem: For the given inhomogeneous differential equation \( y^{\prime \prime}+16 y=\sin (4 x+\alpha), \quad(\alpha= \) const \( ) \) write the form of its particular solution with indefinite coefficients (don't find the numerical values of the coefficients).

8.1.2.21 Second order differential equations

0.77 $

Problem: For the given inhomogeneous differential equation \( y^{\prime \prime}-4 y^{\prime}=2 \cos ^{2} 4 x \) write the form of its particular solution with indefinite coefficients (don't find the numerical values of the coefficients). clip2net.com

8.1.2.22 Second order differential equations

1.03 $

  • ‹
  • 1
  • 2
  • 3
  • 4
  • ›

mathproblemsbank.net

Terms of use Privacy policy

© Copyright 2025, MathProblemsBank

Trustpilot
Order a solution
Order a solution to a problem?
Order a solution
Order a solution to a problem?
home.button.login