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Problem: Solve the differential equation: \[ y=2 x y^{\prime}+\frac{1}{\left(y^{\prime}\right)^{2}} . \]

8.1.1.10 First order differential equations

2.03 $

Problem: Find the general integral of the differential equation: \[ x \sqrt{4+y^{2}} d x+y \sqrt{1+x^{2}} d y=0 . \]

8.1.1.12 First order differential equations

0 $

Problem: Find the general integral of the differential equation: \[ x y^{\prime}=3 \sqrt{x^{2}+y^{2}}+y . \]

8.1.1.13 First order differential equations

1.02 $

Problem: Find a solution to Cauchy problem: \[ y^{\prime}+\frac{y}{x}=3 x, \quad y(1)=1 . \]

8.1.1.14 First order differential equations

0 $

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

8.1.1.15 First order differential equations

1.02 $

Problem: Find a solution to Cauchy problem: \[ 2 x y^{\prime}-3 y=-\left(20 x^{2}+12\right) y^{3}, \quad y(1)=\frac{1}{2 \sqrt{2}} . \]

8.1.1.16 First order differential equations

2.03 $

Problem: Find the general solution of the first order differential equation: \[ y^{\prime}-4 y=e^{2 x} \text {. } \]

8.1.1.17 First order differential equations

1.02 $

Problem: Find the general solution of the differential equation: \[ \left(1+x^{2}\right) d y-2 x y d x=0 . \]

8.1.1.18 First order differential equations

0 $

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

8.1.1.19 First order differential equations

1.27 $

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

1.78 $

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

1.52 $

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

1.27 $

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

1.78 $

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

1.27 $

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

1.52 $

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