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

The solution for (dy)/(dx)=6x^6sqrt(y) is y=(9x^{14}}{49}+\frac{3c_{1}x^7)/7+(c_{1}^2)/4

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(dy)/(dx)=6x^6sqrt(y)

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

y = \frac{9 x ^{14}}{49} + \frac{3 c _{1} x ^{7}}{7} + \frac{c _{1}^{2}}{4}

Solution steps

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

Solve separable ODE:

y = \frac{9 x ^{14}}{49} + \frac{3 c _{1} x ^{7}}{7} + \frac{c _{1}^{2}}{4}

y = \frac{9 x ^{14}}{49} + \frac{3 c _{1} x ^{7}}{7} + \frac{c _{1}^{2}}{4}

y^{^{'}} = e^{3 x + 2 y}, y (0) = 0

\frac{d y}{d x} = 4 e^{x - y}, y (0) = ln (7)

\frac{d y}{d x} = - \frac{6}{4} x^{5} y^{6}

a x^{^{'}} + b x = 0

x y - 2 y - x + 2 - (x y - 2 x - y + 2) \frac{d y}{d x} = 0

What is the solution for (dy)/(dx)=6x^6sqrt(y) ?
The solution for (dy)/(dx)=6x^6sqrt(y) is y=(9x^{14}}{49}+\frac{3c_{1}x^7)/7+(c_{1}^2)/4