What is the solution for (dy)/(dx)=4x^6sqrt(y) ?

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

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(dy)/(dx)=4x^6sqrt(y)

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

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

Solution steps

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

Solve separable ODE:

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

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

\frac{d y}{d x} = \frac{5 x ^{2}}{8 y ^{2}}

\frac{d y}{d x} = x y^{2} e^{x}, y (0) = 2

\frac{d y}{d x} = \frac{x ^{2} - 1}{y ^{2}}, y (0) = 2

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

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

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