What is the solution for (dy)/(dx)+7xy=8x ?

The solution for (dy)/(dx)+7xy=8x is y=(e^{(-7x^2+c_{1})/2})/(7)+8/7

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(dy)/(dx)+7xy=8x

\frac{d y}{d x} + 7 x y = 8 x

y = \frac{e ^{\frac{- 7 x ^{2} + c _{1}}{2}}}{7} + \frac{8}{7}

Solution steps

\frac{d y}{d x} + 7 x y = 8 x

Solve separable ODE:

y = \frac{e ^{\frac{- 7 x ^{2} + c _{1}}{2}}}{7} + \frac{8}{7}

y = \frac{e ^{\frac{- 7 x ^{2} + c _{1}}{2}}}{7} + \frac{8}{7}

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

\frac{d P}{d t} = 0.02 P (1 - \frac{P}{250000})

y^{^{'}} = - 0.00003 (y - 288.03) (y - 961.97)

\frac{d y}{d x} = 4 x (y^{2} + 1)

\frac{d y}{d t} = 4 - y

What is the solution for (dy)/(dx)+7xy=8x ?
The solution for (dy)/(dx)+7xy=8x is y=(e^{(-7x^2+c_{1})/2})/(7)+8/7