What is the solution for 5y^{''}+y^'=-10x,y(0)=0,y^'(0)=-15 ?

The solution for 5y^{''}+y^'=-10x,y(0)=0,y^'(0)=-15 is y=-325+325e^{-x/5}-5x^2+50x

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5y^{''}+y^'=-10x,y(0)=0,y^'(0)=-15

5 y^{^{''}} + y^{^{'}} = - 10 x, y (0) = 0, y^{^{'}} (0) = - 15

y = - 325 + 325 e^{- \frac{x}{5}} - 5 x^{2} + 50 x

Solution steps

5 y^{''} (x) + y^{'} (x) = - 10 x

Solve linear ODE:

y = - 325 + 325 e^{- \frac{x}{5}} - 5 x^{2} + 50 x

y = - 325 + 325 e^{- \frac{x}{5}} - 5 x^{2} + 50 x

f (x) = \frac{2 x + 1}{x + 2}, (1, 1)

\int (x \cdot (1 - x^{4})) d x

\frac{d y}{d x} = y^{2} x^{3}

\int \frac{2}{2 + e ^{x}} d x

x \to 3 lim (7 - 3 x)

What is the solution for 5y^{''}+y^'=-10x,y(0)=0,y^'(0)=-15 ?
The solution for 5y^{''}+y^'=-10x,y(0)=0,y^'(0)=-15 is y=-325+325e^{-x/5}-5x^2+50x