What is the solution for (dy)/(dx)=((5x^6))/(y^2),y(0)=1 ?

The solution for (dy)/(dx)=((5x^6))/(y^2),y(0)=1 is y=\sqrt[3]{(15x^7)/7+1}

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(dy)/(dx)=((5x^6))/(y^2),y(0)=1

\frac{d y}{d x} = \frac{( 5 x ^{6} )}{y ^{2}}, y (0) = 1

y = 3 \frac{15 x ^{7}}{7} + 1

Solution steps

\frac{d y}{d x} = \frac{( 5 x ^{6} )}{y ^{2}}

Solve separable ODE:

y = 3 \frac{15 x ^{7}}{7} + 1

y = 3 \frac{15 x ^{7}}{7} + 1

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

y^{^{'}} = - 2 \cdot t \cdot y^{2}, y (0) = 1

x^{\frac{1}{3}} y^{^{'}} + y = 0

y^{^{'}} = x y^{3} \cdot (1 + x^{2})^{(\frac{- 1}{2})}

3 y^{2} d y - t d t = 0

What is the solution for (dy)/(dx)=((5x^6))/(y^2),y(0)=1 ?
The solution for (dy)/(dx)=((5x^6))/(y^2),y(0)=1 is y=\sqrt[3]{(15x^7)/7+1}