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Problem: Find the general solution of the differential equation: \[ \frac{y y^{\prime \prime}-\left(y^{\prime}\right)^{2}}{y \sqrt{x}}=15 y \text {. } \] clip22net.com

8.1.2.40 Second order differential equations

1.78 $

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

8.1.1.41 First order differential equations

1.52 $

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

8.1.1.42 First order differential equations

1.52 $

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

8.1.1.43 First order differential equations

1.52 $

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

8.1.1.44 First order differential equations

1.02 $

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

8.1.2.45 Second order differential equations

1.52 $

Problem: Find the value of the particular solution of the differential equation at the point \( x_{0} \), satisfying given initial conditions: \[ y^{\prime \prime}=2 \sin x \cdot \cos ^{2} x, y(0)=-\frac{5}{9}, \quad y^{\prime}(0)=-\frac{2}{3}, \quad x_{0}=\frac{\pi}{2} . \] clip2net.com

8.1.2.46 Second order differential equations

1.27 $

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

8.1.2.47 Second order differential equations

2.03 $

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

8.1.1.48 First order differential equations

1.52 $

Problem: Find the particular solution of the differential equation: \[ \frac{d^{2} u}{d x^{2}}+5 u=0, \quad u(0)=1, \quad u(1)=7 . \] clip2net.com

8.1.2.49 Second order differential equations

1.27 $

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

8.1.1.50 First order differential equations

1.02 $

Problem: Solve the equation using the formula that reduces multiple integration to single one: \[ x y^{I V}+y^{\prime \prime \prime}=e^{x} \text {. } \]

8.1.3.51 Higher order differential equations

2.03 $

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

8.1.1.52 First order differential equations

0 $

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

8.1.1.53 First order differential equations

1.27 $

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

8.1.1.54 First order differential equations

1.52 $

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