What is the solution for (dy)/(dx)=y(7x^2+5) ?

The solution for (dy)/(dx)=y(7x^2+5) is y=e^{(7x^3)/3+5x+c_{1}}

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(dy)/(dx)=y(7x^2+5)

\frac{d y}{d x} = y (7 x^{2} + 5)

y = e^{\frac{7 x ^{3}}{3} + 5 x + c_{1}}

Solution steps

\frac{d y}{d x} = y (7 x^{2} + 5)

Solve separable ODE:

y = e^{\frac{7 x ^{3}}{3} + 5 x + c_{1}}

y = e^{\frac{7 x ^{3}}{3} + 5 x + c_{1}}

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

x^{2} \cdot y^{^{'}} - y = 0

\frac{d y}{d x} = \frac{1}{4} e^{- 2 y}, y (0) = 0

\frac{d y}{d x} = \frac{( 2 y ln ( y ) )}{( x )}, y (1) = 4

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

What is the solution for (dy)/(dx)=y(7x^2+5) ?
The solution for (dy)/(dx)=y(7x^2+5) is y=e^{(7x^3)/3+5x+c_{1}}