First order differential equations

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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

1.53 $

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

1.53 $

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

1.53 $

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 first order differential equation: \[ y^{\prime}-\frac{y}{\sin x}=\cos ^{2} x \text {. } \]

8.1.1.48 First order differential equations

1.53 $

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: 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

1.53 $

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

2.04 $

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

2.55 $

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 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

3.31 $

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