What is the solution for (dy)/(dx)+6x^2y=7x^2,y(0)=2 ?

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

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(dy)/(dx)+6x^2y=7x^2,y(0)=2

\frac{d y}{d x} + 6 x^{2} y = 7 x^{2}, y (0) = 2

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

Solution steps

\frac{d y}{d x} + 6 x^{2} y = 7 x^{2}

Solve separable ODE:

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

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

\frac{2 d y}{d t} + y = 0

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

\frac{d y}{d x} = \frac{e ^{8 y + x}}{x}, x > 0

y^{^{'}} = 8 x sec (y)

e^{x} tan (y) d x + (1 - e^{x}) sec^{2} (y) d y = 0

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