What is the solution for (x+3)^2y+(x+3)y^'-y=0 ?

The solution for (x+3)^2y+(x+3)y^'-y=0 is y=e^{-1/2 x^2-3x-9/2+c_{1}}x+3e^{-1/2 x^2-3x-9/2+c_{1}}

Popular >

(x+3)^2y+(x+3)y^'-y=0

(x + 3)^{2} y + (x + 3) y^{^{'}} - y = 0

y = e^{- \frac{1}{2} x^{2} - 3 x - \frac{9}{2} + c_{1}} x + 3 e^{- \frac{1}{2} x^{2} - 3 x - \frac{9}{2} + c_{1}}

Solution steps

(x + 3)^{2} y + (x + 3) y^{'} (x) - y = 0

Solve separable ODE:

y = e^{- \frac{1}{2} x^{2} - 3 x - \frac{9}{2} + c_{1}} x + 3 e^{- \frac{1}{2} x^{2} - 3 x - \frac{9}{2} + c_{1}}

y = e^{- \frac{1}{2} x^{2} - 3 x - \frac{9}{2} + c_{1}} x + 3 e^{- \frac{1}{2} x^{2} - 3 x - \frac{9}{2} + c_{1}}

\frac{d x}{d t} = 2 t x

\frac{d}{d t} ((y) (8 y - y^{2})) = - \frac{8}{144} y, y (0) = 8

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

y^{^{'}} sec (x) = y^{2}, y (\frac{13 π}{2}) = \frac{1}{3}

\frac{d y}{d x} = - 16 x y

What is the solution for (x+3)^2y+(x+3)y^'-y=0 ?
The solution for (x+3)^2y+(x+3)y^'-y=0 is y=e^{-1/2 x^2-3x-9/2+c_{1}}x+3e^{-1/2 x^2-3x-9/2+c_{1}}