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Problem: Find the general solution of the differential equation: \[ y^{\prime \prime}+5 y^{\prime}-14 y=e^{2 x}\left(2 x^{3}-3 x-1\right) . \] clip2net.com

8.1.2.87 Second order differential equations

1.78 $

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

1.78 $

Problem: Find the general solution of the differential equation: \[ y^{\prime}-x y^{2}=0 \text {. } \]

8.1.1.89 First order differential equations

0 $

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

8.1.1.90 First order differential equations

1.27 $

Problem: Find the general integral of the differential equation: \[ (x-y) d y-x d x=0 . \]

8.1.1.91 First order differential equations

1.78 $

Problem: Find the solution of the Cauchy problem for the differential equation: \[ y^{\prime}-\frac{y}{x}=-2 \frac{\ln x}{x}, \quad y(1)=1 . \]

8.1.1.92 First order differential equations

1.53 $

Problem: Find the solution of the Cauchy problem for the differential equation: \[ 2\left(y^{\prime}+y\right)=x y^{2}, \quad y(0)=2 . \]

8.1.1.93 First order differential equations

2.03 $

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

1.53 $

Problem: Find the general solution of the given equations, knowing their particular solutions. In those problems where the particular solution is not given, we can look for it by selecting, for example, in the form of an exponential function \( y_{1}=e^{a x} \) or algebraic polynomial \( y_{1}=x^{n}+a x^{n-1}+b x^{n-2}+\cdots \). \[ \begin{array}{l} \left(x^{2}-2 x+3\right) y^{\prime \prime \prime}-\left(x^{2}+1\right) y^{\prime \prime}+2 x y^{\prime}-2 y=0, \\ y_{1}=x, y_{2}=e^{x} . \end{array} \]

8.1.3.95 Higher order differential equations

3.81 $

Problem: Find the general solution of the differential equation: \[ 2 x^{4} y y^{\prime}+y^{4}=4 x^{6} \text {. } \]

8.1.1.96 First order differential equations

3.05 $

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

1.27 $

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

2.54 $

Problem: Find the solution to the Cauchy problem for the linear partial differential equation: \[ \cos y \cdot \frac{\partial z}{\partial x}+\cos x \cdot \frac{\partial z}{\partial y}=0, \quad z(0 ; y)=\sin ^{2} y . \]

11.4.7 First order partial differential equations

3.81 $

Problem: Determine the type of the second order equation: \[ u_{x x}+2 u_{x y}-2 u_{y z}+2 u_{y y}+2 u_{z z}=0 . \]

11.5.4.5 With constant coefficients

0 $

Problem: Determine the type of the second order equation: \[ u_{x y}+u_{x z}+u_{x t}+u_{z t}=0 . \]

11.5.4.6 With constant coefficients

1.53 $

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