What is the solution for (dy)/(dx)=2x^4sqrt(y),y>0 ?

The solution for (dy)/(dx)=2x^4sqrt(y),y>0 is y=(x^{10}}{25}+\frac{c_{1}x^5)/5+(c_{1}^2)/4

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(dy)/(dx)=2x^4sqrt(y),y>0

\frac{d y}{d x} = 2 x^{4} y, y > 0

y = \frac{x ^{10}}{25} + \frac{c _{1} x ^{5}}{5} + \frac{c _{1}^{2}}{4}

Solution steps

\frac{d y}{d x} = 2 x^{4} y

Solve separable ODE:

y = \frac{x ^{10}}{25} + \frac{c _{1} x ^{5}}{5} + \frac{c _{1}^{2}}{4}

y = \frac{x ^{10}}{25} + \frac{c _{1} x ^{5}}{5} + \frac{c _{1}^{2}}{4}

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

\frac{d y}{d x} = 2 x cos^{2} (y), y (0) = \frac{π}{4}

(x + 1) d x + e^{y} d y = 0

y^{^{'}} = y - \frac{y ^{2}}{3}

\frac{d y}{d x} = \frac{1 + 2 y}{4 - x ^{2}}

What is the solution for (dy)/(dx)=2x^4sqrt(y),y>0 ?
The solution for (dy)/(dx)=2x^4sqrt(y),y>0 is y=(x^{10}}{25}+\frac{c_{1}x^5)/5+(c_{1}^2)/4