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Popular >

y^{''}-9y=54t

Solution

y^{^{''}} - 9 y = 54 t

Solution

y = c_{1} e^{3 t} + c_{2} e^{- 3 t} - 6 t

Solution steps

y^{''} (t) - 9 y = 54 t

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{- 3 t} - 6 t

y = c_{1} e^{3 t} + c_{2} e^{- 3 t} - 6 t

Graph

Popular Examples

y^{''}+10y^'+25y=(e^{-5x})/(x^6)

y^{^{''}} + 10 y^{^{'}} + 25 y = \frac{e ^{- 5 x}}{x ^{6}}

y^{''}-4y^'+8y=12xe^{2x}+6e^{2x}

y^{^{''}} - 4 y^{^{'}} + 8 y = 12 x e^{2 x} + 6 e^{2 x}

y^{''}+y=8xcos(x)

y^{^{''}} + y = 8 x cos (x)

(D^2-6D+9)y=x^2e^{2x}

(D^{2} - 6 D + 9) y = x^{2} e^{2 x}

y^{''}+2y^'+10=0,y(0)=-2,y^'(0)=0

y^{^{''}} + 2 y^{^{'}} + 10 = 0, y (0) = - 2, y^{^{'}} (0) = 0

Frequently Asked Questions (FAQ)

What is the solution for y^{''}-9y=54t ?
The solution for y^{''}-9y=54t is y=c_{1}e^{3t}+c_{2}e^{-3t}-6t