What is the solution for (dy)/(dx)+6x^2y=5x^2,y(0)=4 ?

The solution for (dy)/(dx)+6x^2y=5x^2,y(0)=4 is y=(19e^{-2x^3})/6+5/6

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(dy)/(dx)+6x^2y=5x^2,y(0)=4

\frac{d y}{d x} + 6 x^{2} y = 5 x^{2}, y (0) = 4

y = \frac{19 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{19 e ^{- 2 x^{3}}}{6} + \frac{5}{6}

y = \frac{19 e ^{- 2 x^{3}}}{6} + \frac{5}{6}

y^{^{'}} = x y - 2 x + y - 2

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

y^{^{'}} = \frac{2}{3} x 1 - 9 y^{2}, y (0) = 0

(x + 1) y^{^{'}} - 3 y = 0

\frac{d y}{d x} x^{2} + y^{2} = 77

What is the solution for (dy)/(dx)+6x^2y=5x^2,y(0)=4 ?
The solution for (dy)/(dx)+6x^2y=5x^2,y(0)=4 is y=(19e^{-2x^3})/6+5/6