What is the solution for (dy)/(dx)=3x^6sqrt(y),y>0 ?

The solution for (dy)/(dx)=3x^6sqrt(y),y>0 is y=(9x^{14}}{196}+(3c_{1}x^7)/(14)+\frac{c_{1}^2)/4

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(dy)/(dx)=3x^6sqrt(y),y>0

\frac{d y}{d x} = 3 x^{6} y, y > 0

y = \frac{9 x ^{14}}{196} + \frac{3 c _{1} x ^{7}}{14} + \frac{c _{1}^{2}}{4}

Solution steps

\frac{d y}{d x} = 3 x^{6} y

Solve separable ODE:

y = \frac{9 x ^{14}}{196} + \frac{3 c _{1} x ^{7}}{14} + \frac{c _{1}^{2}}{4}

y = \frac{9 x ^{14}}{196} + \frac{3 c _{1} x ^{7}}{14} + \frac{c _{1}^{2}}{4}

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

\frac{d P}{d t} = 8 Pt, P (1) = 2

(x y^{2} + y^{2}) d x + x d y = 0

\frac{d y}{d x} + 3 e^{x + y} = 0

y^{^{'}} = sin (x) cos^{2} (x) tan (y)

What is the solution for (dy)/(dx)=3x^6sqrt(y),y>0 ?
The solution for (dy)/(dx)=3x^6sqrt(y),y>0 is y=(9x^{14}}{196}+(3c_{1}x^7)/(14)+\frac{c_{1}^2)/4