First order differential equations

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Problem: Find the general solution of the differential equation: \[ 2 x^{4} y y^{\prime}+y^{4}=4 x^{6} \text {. } \]

8.1.1.96 First order differential equations

3.06 $

Problem: Solve the differential equation: \[ y^{\prime}=(4 x+y+1)^{2} \text {. } \]

8.1.1.3 First order differential equations

1.27 $

Problem: Write an equation, which is satisfied by all extremum points of the integral curves of the differential equation \( y^{\prime}=f(x, y) \). How to differentiate maximum points from minimum points?

8.1.1.4 First order differential equations

1.27 $

Problem: Write an equation, which is satisfied by all the inflection points of the curves of the differential equation \( y^{\prime}=f(x, y) \) and, particularly, the differential equation

8.1.1.5 First order differential equations

1.02 $

Problem: Solve the differential equation: \[ (2 x-y+1) d x+(2 y-x-1) d y=0 . \]

8.1.1.6 First order differential equations

2.04 $

Problem: Solve the differential equation: \[ y^{\prime}=\frac{y}{x+y^{3}} \text {. } \]

8.1.1.7 First order differential equations

1.27 $

Problem: Solve the differential equation: \[ y^{\prime}=\frac{2 x}{x^{2} \cos y+\sin 2 y} \text {. } \]

8.1.1.8 First order differential equations

1.53 $

Problem: Solve the differential equation: \[ y=\left(y^{\prime}\right)^{2}+4\left(y^{\prime}\right)^{3} . \]

8.1.1.9 First order differential equations

1.27 $

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

2.04 $

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

2.04 $

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 $

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