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Popular >

y^{''}-2y^'+y=2000x^2-150e^x

Solution

y^{^{''}} - 2 y^{^{'}} + y = 2000 x^{2} - 150 e^{x}

Solution

y = c_{1} e^{x} + c_{2} x e^{x} + 2000 x^{2} + 8000 x + 12000 - 75 x^{2} e^{x}

Solution steps

y^{''} (x) - 2 y^{'} (x) + y = 2000 x^{2} - 150 e^{x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + 2000 x^{2} + 8000 x + 12000 - 75 x^{2} e^{x}

y = c_{1} e^{x} + c_{2} x e^{x} + 2000 x^{2} + 8000 x + 12000 - 75 x^{2} e^{x}

Graph

Popular Examples

y^{'''}+3y^{''}+3y^'+y=2e^{-x}

y^{^{'''}} + 3 y^{^{''}} + 3 y^{^{'}} + y = 2 e^{- x}

y^{''}+8y^'+12y=1-u,y(0)=0,y^'(0)=0

y^{^{''}} + 8 y^{^{'}} + 12 y = 1 - u, y (0) = 0, y^{^{'}} (0) = 0

-y^{''}-4y^'+4y=e-3t

- y^{^{''}} - 4 y^{^{'}} + 4 y = e - 3 t

y^{''}+7y^'+14y=1096*e^{2t}*cos(8t)

y^{^{''}} + 7 y^{^{'}} + 14 y = 1096 \cdot e^{2 t} \cdot cos (8 t)

x^{''}-2x^'+x=1t^2e^t

x^{^{''}} - 2 x^{^{'}} + x = 1 t^{2} e^{t}

Frequently Asked Questions (FAQ)

What is the solution for y^{''}-2y^'+y=2000x^2-150e^x ?
The solution for y^{''}-2y^'+y=2000x^2-150e^x is y=c_{1}e^x+c_{2}xe^x+2000x^2+8000x+12000-75x^2e^x