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Popular >

y^{''}+4y=11t^3sin(2t)

Solution

y^{^{''}} + 4 y = 11 t^{3} sin (2 t)

Solution

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{- 11 cos ( 2 t ) ( 64 t ^{4} sin ^{2} ( 2 t ) + 32 t ^{4} cos ( 4 t ) - 32 t ^{3} sin ( 4 t ) - 24 t ^{2} cos ( 4 t ) + 12 t sin ( 4 t ) + 3 cos ( 4 t ) ) + 11 sin ( 2 t ) ( - 32 t ^{3} cos ( 4 t ) + 3 ( 8 t ^{2} sin ( 4 t ) + 4 t cos ( 4 t ) - sin ( 4 t ) ) )}{512}

Solution steps

y^{''} (t) + 4 y = 11 t^{3} sin (2 t)

Solve linear ODE:

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{- 11 cos ( 2 t ) ( 64 t ^{4} sin ^{2} ( 2 t ) + 32 t ^{4} cos ( 4 t ) - 32 t ^{3} sin ( 4 t ) - 24 t ^{2} cos ( 4 t ) + 12 t sin ( 4 t ) + 3 cos ( 4 t ) ) + 11 sin ( 2 t ) ( - 32 t ^{3} cos ( 4 t ) + 3 ( 8 t ^{2} sin ( 4 t ) + 4 t cos ( 4 t ) - sin ( 4 t ) ) )}{512}

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{- 11 cos ( 2 t ) ( 64 t ^{4} sin ^{2} ( 2 t ) + 32 t ^{4} cos ( 4 t ) - 32 t ^{3} sin ( 4 t ) - 24 t ^{2} cos ( 4 t ) + 12 t sin ( 4 t ) + 3 cos ( 4 t ) ) + 11 sin ( 2 t ) ( - 32 t ^{3} cos ( 4 t ) + 3 ( 8 t ^{2} sin ( 4 t ) + 4 t cos ( 4 t ) - sin ( 4 t ) ) )}{512}

Graph

Popular Examples

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

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

y^{''}-3y^'-4y=4x

y^{^{''}} - 3 y^{^{'}} - 4 y = 4 x

y^{''}-2y^'+5y=-8,y(0)=2,y^'(0)=2

y^{^{''}} - 2 y^{^{'}} + 5 y = - 8, y (0) = 2, y^{^{'}} (0) = 2

1/2 y^{''}+2y=2tan(2t)-1/2 e^t

\frac{1}{2} y^{^{''}} + 2 y = 2 tan (2 t) - \frac{1}{2} e^{t}

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

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

Frequently Asked Questions (FAQ)

What is the solution for y^{''}+4y=11t^3sin(2t) ?
The solution for y^{''}+4y=11t^3sin(2t) is