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

8.1.3.55 Higher order differential equations

1.52 $

Problem: Find the particular solution of the differential equation: \[ 2 x y^{\prime}-3 y=-\left(20 x^{2}+12\right) y^{3}, \quad y(1)=\frac{1}{2 \sqrt{2}} . \]

8.1.1.56 First order differential equations

2.03 $

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

8.1.1.57 First order differential equations

1.78 $

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

8.1.1.58 First order differential equations

2.54 $

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

8.1.1.59 First order differential equations

0 $

Problem: Find the particular solution of the differential equations: \[ y^{\prime}+\frac{x y}{2\left(1-x^{2}\right)}=\frac{x}{2}, \quad y(0)=\frac{2}{3} . \]

8.1.1.60 First order differential equations

1.78 $

Problem: Find the general solution of the higher order differential equation: \[ y^{\prime \prime \prime}-81 y^{\prime}=162 e^{9 x}+81 \sin 9 x \text {. } \]

8.1.3.61 Higher order differential equations

1.78 $

Problem: Find the general solution of the differential equations: \[ x\left(y^{\prime}\right)^{2}=y^{\prime}-\frac{3}{4} e-2 y \text {. } \]

8.1.1.62 First order differential equations

3.3 $

Problem: Find the particular solution of the differential equation: \[ y^{\prime \prime}-9 y^{\prime}=e^{3 x} \cos x \text {. } \] clip2net.com

8.1.2.63 Second order differential equations

2.03 $

Problem: Find the general solution of the first order inhomogeneous differential equation: \[ \left(x^{4}+x\right) y^{\prime}+\left(2 x^{3}-1\right) y=\frac{x^{3}-2}{x} \text {. } \]

8.1.1.65 First order differential equations

1.52 $

Problem: Find the general solution of the higher order differential equation: \[ y^{(4)}=\cos 5 x \text {. } \]

8.1.3.66 Higher order differential equations

0 $

Problem: Find the particular solution of the differential equation: \[ y^{\prime \prime} \cdot y^{3}+1=0, \quad y(-2)=-1, \quad y^{\prime}(-2)=2 . \] clip2net.com

8.1.2.67 Second order differential equations

1.78 $

Problem: Find the general solution of the corresponding homogeneous differential equation and the form of the particular solution for the higher order differential equation: \[ y^{(4)}-2 y^{\prime \prime \prime}+y^{\prime}-2 y=\left(x^{2}+x\right) e^{2 x}+1 \text {. } \] clip2net.com

8.1.3.68 Higher order differential equations

1.78 $

Problem: Find the general solution of the second order differential equation: \[ y^{\prime \prime}+16 y^{\prime}+13 y=4 e^{-3 x} \text {. } \] clip2net.com

8.1.2.69 Second order differential equations

1.52 $

Problem: Find the solution of the Cauchy problem or the second order differential equation: \[ y^{\prime \prime}+2 y^{\prime}+5 y=5 x^{2}-x, \quad y(0)=1, \quad y^{\prime}(0)=0 \text {. } \] clip2net.com

8.1.2.70 Second order differential equations

1.52 $

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