First order differential equations

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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

1.53 $

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

1.27 $

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

1.02 $

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

1.27 $

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

1.53 $

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

1.53 $

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

1.27 $

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

1.27 $

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

8.1.1.89 First order differential equations

0 $

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

8.1.1.90 First order differential equations

1.27 $

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

8.1.1.91 First order differential equations

1.78 $

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

8.1.1.92 First order differential equations

1.53 $

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

8.1.1.93 First order differential equations

2.04 $

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