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Popular >

(d^2y)/(dt^2)-4y=tcos(2t)

Solution

\frac{d ^{2} y}{d t ^{2}} - 4 y = t cos (2 t)

Solution

y = c_{1} e^{2 t} + c_{2} e^{- 2 t} - \frac{t cos ( 2 t )}{8} + \frac{1}{16} sin (2 t)

Solution steps

\frac{d ^{2} y}{d t ^{2}} - 4 y = t cos (2 t)

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} e^{- 2 t} - \frac{t cos ( 2 t )}{8} + \frac{1}{16} sin (2 t)

y = c_{1} e^{2 t} + c_{2} e^{- 2 t} - \frac{t cos ( 2 t )}{8} + \frac{1}{16} sin (2 t)

Popular Examples

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4 y^{^{''}} - 8 y^{^{'}} + 8 y = e^{x} sec (x)

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

Frequently Asked Questions (FAQ)

What is the solution for (d^2y)/(dt^2)-4y=tcos(2t) ?
The solution for (d^2y)/(dt^2)-4y=tcos(2t) is y=c_{1}e^{2t}+c_{2}e^{-2t}-(tcos(2t))/8+1/16 sin(2t)