Higher order differential equations

MathProblemsBank banner

MathProblemsBank banner

Math Problems and solutions

Problem list Free problems

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

Problem: Find the general solution of the differential equation: \[ y^{\prime \prime \prime}+4 y^{\prime \prime}+4 y^{\prime}=0 \text {. } \]

8.1.3.97 Higher order differential equations

1.28 $

Problem: Find the general solution of the differential equation: \[ y^{\prime \prime \prime}-3 y^{\prime \prime}-y^{\prime}+3 y=(4-8 x) e^{x} \text {. } \]

8.1.3.1 Higher order differential equations

1.54 $

Problem: Find the general solution of the equation \( x^{3} y^{\prime \prime \prime}+ \) \( +5 x^{2} y^{\prime \prime}+2 x y^{\prime}-2 y=0 \), if its two particular solutions are known \( y_{1}=x \) and \( y_{2}=1 / x \). clip2net.com

8.1.3.2 Higher order differential equations

3.85 $

Problem: Investigate linear dependence for the following system of functions: \( \sin 2 x, \sin x, \cos x \). clip2net.com

8.1.3.3 Higher order differential equations

0.77 $

Problem: Investigate linear dependence for the following system of functions: \( x, 2 x, x^{2} \).

8.1.3.4 Higher order differential equations

0 $

Problem: Investigate linear dependence for the following system of functions: \( e^{x}, x e^{x}, x^{2} e^{x} \).

8.1.3.5 Higher order differential equations

0 $

Problem: Investigate linear dependence for the following system of functions: \( \operatorname{ch} x, \operatorname{sh} x \).

8.1.3.6 Higher order differential equations

0.77 $

Problem: Investigate linear dependence for the following system of functions: \( e^{x}, e^{x+1} \). clip2net.com

8.1.3.7 Higher order differential equations

0 $

Problem: Investigate linear dependence for the following system of functions: \( x, 0, e^{x} \).

8.1.3.8 Higher order differential equations

0 $

Problem: Investigate linear dependence for the following system of functions: \( 1, \sin x, \cos 2 x \).

8.1.3.10 Higher order differential equations

0.77 $

Problem: Knowing the fundamental system of solutions of the linear homogeneous differential equation, \( e^{2 x} \cos x, e^{2 x} \sin x \), write this equation. clip2net.com

8.1.3.11 Higher order differential equations

1.28 $

Problem: Knowing the fundamental system of solutions of the linear homogeneous differential equation, \( x^{3}, x^{4} \), write this equation. clip22net.com

8.1.3.12 Higher order differential equations

1.28 $

Problem: Knowing the fundamental system of solutions of the linear homogeneous differential equation, \( 2 x, x--2, e^{x}+1 \), write this equation.

8.1.3.18 Higher order differential equations

1.28 $

Problem: Knowing the fundamental system of solutions of the linear homogeneous differential equation, \( e^{2 x}, \sin x, \cos x \), write this equation. clip2net.com

8.1.3.19 Higher order differential equations

1.28 $

Problem: Knowing the fundamental system of solutions \( e^{x}, \sin x, \cos x \) of the linear homogeneous differential equation, find its particular solution that satisfies the initial conditions: \[ y(0)=3, y^{\prime}(0)=4, y^{\prime \prime}(0)=-1 \text {. } \]

8.1.3.20 Higher order differential equations

1.28 $

‹
1
2
3
›