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Popular >

y^{''}-5y^'+6y=xe^{-2x}

Solution

y^{^{''}} - 5 y^{^{'}} + 6 y = x e^{- 2 x}

Solution

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{e ^{- 2 x} x}{20} + \frac{9}{400} e^{- 2 x}

Solution steps

y^{''} (x) - 5 y^{'} (x) + 6 y = x e^{- 2 x}

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{e ^{- 2 x} x}{20} + \frac{9}{400} e^{- 2 x}

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{e ^{- 2 x} x}{20} + \frac{9}{400} e^{- 2 x}

Graph

Popular Examples

(d^{3} - 3 d) y = 9 x^{2}

y^{''}+y^'-12y=4e^xsin(2x)+4e^{3x}+2

y^{^{''}} + y^{^{'}} - 12 y = 4 e^{x} sin (2 x) + 4 e^{3 x} + 2

(d^2y)/(dx^2)+(dy)/(dx)+2y=5e^{3x}

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} + 2 y = 5 e^{3 x}

(d^2y)/(dx^2)+2(dy)/(dx)-15y=(x+1)e^x

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} - 15 y = (x + 1) e^{x}

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

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

Frequently Asked Questions (FAQ)

What is the solution for y^{''}-5y^'+6y=xe^{-2x} ?
The solution for y^{''}-5y^'+6y=xe^{-2x} is y=c_{1}e^{3x}+c_{2}e^{2x}+(e^{-2x}x)/(20)+9/400 e^{-2x}