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

8.1.3.71 Higher order differential equations

1.75 $

Problem: Find the general solution of the linear homogeneous equation by the given particular solution \( y_{1} \) corresponding to the linear homogeneous equation: \[ y^{\prime \prime}-2(\tan x+1) y^{\prime}+(2 \tan x+1) y=2 e^{x} \sec ^{4} x, y_{1}=e^{x} . \] clip2net.com

8.1.2.72 Second order differential equations

3 $

Problem: Find the general solution of the differential equation: \[ \sqrt{y} d x+\sqrt{x} d y=0 . \]

8.1.1.73 First order differential equations

0 $

Problem: Find the general solution of the differential equation: \[ x^{2} y^{\prime}-2 x y=3 y \text {. } \]

8.1.1.74 First order differential equations

1.25 $

Problem: Find the solution of the Cauchy problem for the differential equation: \[ y^{\prime \prime}+4 y=\sin 2 x+1, \quad y(0)=\frac{1}{4}, \quad y^{\prime}(0)=0 . \] clip22net.com

8.1.2.75 Second order differential equations

2 $

Problem: Find the solution of the differential equation: \[ \sqrt{x} d y=\sqrt{y} d x \text {. } \]

8.1.1.76 First order differential equations

0 $

Problem: Find the solution of the Cauchy problem for the differential equation: \[ \left(1+e^{2 x}\right) y^{2} d y=e^{x} d x, \quad y(0)=0 . \]

8.1.1.77 First order differential equations

1 $

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

8.1.1.78 First order differential equations

1.25 $

Problem: Find the general solution to the differential equation: \[ \left(1+x^{2}\right) y^{\prime}+y=\tan ^{-1} x \text {. } \]

8.1.1.79 First order differential equations

1.5 $

Problem: Find the general solution of the differential equation: \[ \left(x^{2}+y\right) d x+(x-2 y) d y=0 . \]

8.1.1.80 First order differential equations

1.5 $

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

8.1.2.81 Second order differential equations

1.5 $

Problem: Find the general solution of the differential equation: \[ y^{\prime \prime}+y=\tan x \text {. } \] clip2net.com

8.1.2.82 Second order differential equations

1.75 $

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

8.1.1.84 First order differential equations

1.25 $

Problem: Find the general solution of the differential equation: \[ y^{\prime}-2 x y=1-2 x^{2} \text {. } \]

8.1.1.85 First order differential equations

1.25 $

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

8.1.2.86 Second order differential equations

1.25 $

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