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

The solution for (dy)/(dx)+6x^2y=5x^2,y(0)=2 is y=(7e^{-2x^3})/6+5/6

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

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

y = \frac{7 e ^{- 2 x^{3}}}{6} + \frac{5}{6}

Solution steps

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

Solve separable ODE:

y = \frac{7 e ^{- 2 x^{3}}}{6} + \frac{5}{6}

y = \frac{7 e ^{- 2 x^{3}}}{6} + \frac{5}{6}

\frac{d y}{d x} = sin (x) (1 - cos (x)) (y^{2} - 4)

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

(x^{2} + 1) tan (y) y^{^{'}} = x

\frac{d y}{d t} = \frac{6 t ^{2}}{7 y}

\frac{d y}{d x} = 64 y x^{7}

What is the solution for (dy)/(dx)+6x^2y=5x^2,y(0)=2 ?
The solution for (dy)/(dx)+6x^2y=5x^2,y(0)=2 is y=(7e^{-2x^3})/6+5/6