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

The solution for (dy)/(dx)=2x^5sqrt(y) is y=(x^{12}}{36}+\frac{c_{1}x^6)/6+(c_{1}^2)/4

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

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

y = \frac{x ^{12}}{36} + \frac{c _{1} x ^{6}}{6} + \frac{c _{1}^{2}}{4}

Solution steps

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

Solve separable ODE:

y = \frac{x ^{12}}{36} + \frac{c _{1} x ^{6}}{6} + \frac{c _{1}^{2}}{4}

y = \frac{x ^{12}}{36} + \frac{c _{1} x ^{6}}{6} + \frac{c _{1}^{2}}{4}

\frac{d N}{d t} + N = N \cdot t e^{t + 2}

\frac{d y}{d x} = \frac{( y x + 5 x )}{x ^{2} + 1}

y^{^{'}} - 3 y sin (3 t) = - 3 sin (3 t), y (\frac{π}{6}) = 2

y^{^{'}} = \frac{y ^{2}}{4}

\frac{d P}{d t} = 0.015 P

What is the solution for (dy)/(dx)=2x^5sqrt(y) ?
The solution for (dy)/(dx)=2x^5sqrt(y) is y=(x^{12}}{36}+\frac{c_{1}x^6)/6+(c_{1}^2)/4