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

The solution for (dy)/(dx)=x^5sqrt(y) is y=(x^{12}}{144}+(c_{1}x^6)/(12)+\frac{c_{1}^2)/4

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

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

y = \frac{x ^{12}}{144} + \frac{c _{1} x ^{6}}{12} + \frac{c _{1}^{2}}{4}

Solution steps

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

Solve separable ODE:

y = \frac{x ^{12}}{144} + \frac{c _{1} x ^{6}}{12} + \frac{c _{1}^{2}}{4}

y = \frac{x ^{12}}{144} + \frac{c _{1} x ^{6}}{12} + \frac{c _{1}^{2}}{4}

y^{^{'}} = t y^{\frac{1}{2}}

(t^{2} + 5 t) x^{^{'}} = 5 x + 5, x (1) = 6

y^{^{'}} = \frac{1}{5} y cos^{2} (y)

y^{^{'}} + 2 y - 4 = 0

\frac{d y}{d x} + ln (x) \cdot y = 3 \cdot ln (x)

What is the solution for (dy)/(dx)=x^5sqrt(y) ?
The solution for (dy)/(dx)=x^5sqrt(y) is y=(x^{12}}{144}+(c_{1}x^6)/(12)+\frac{c_{1}^2)/4