What is the solution for 6y(dy)/(dx)=5x^2 ?

The solution for 6y(dy)/(dx)=5x^2 is y=(sqrt(5x^3+c_{1)})/3 ,y=-(sqrt(5x^3+c_{1)})/3

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6y(dy)/(dx)=5x^2

6 y \frac{d y}{d x} = 5 x^{2}

y = \frac{5 x ^{3} + c _{1}}{3}, y = - \frac{5 x ^{3} + c _{1}}{3}

Solution steps

6 y \frac{d y}{d x} = 5 x^{2}

Solve separable ODE:

y = \frac{5 x ^{3} + c _{1}}{3}, y = - \frac{5 x ^{3} + c _{1}}{3}

y = \frac{5 x ^{3} + c _{1}}{3}, y = - \frac{5 x ^{3} + c _{1}}{3}

2 x y d x + 3 x^{2} d y = 0

\frac{d}{d x} (x^{2} + y^{2}) = 16

\frac{d y}{d x} + 2 \cdot y = 0

\frac{d y}{e ^{y + 3}} = d t \cdot e^{t}

\frac{1 + x ^{2}}{1 + y} \frac{d y}{d x} = - x

What is the solution for 6y(dy)/(dx)=5x^2 ?
The solution for 6y(dy)/(dx)=5x^2 is y=(sqrt(5x^3+c_{1)})/3 ,y=-(sqrt(5x^3+c_{1)})/3