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Popular >

y^{''}+49y=4t^3sin(7t)

Solution

y^{^{''}} + 49 y = 4 t^{3} sin (7 t)

Solution

y = c_{1} cos (7 t) + c_{2} sin (7 t) + (- \frac{1}{7} t^{4} sin^{2} (7 t) + \frac{1}{67228} (- 4802 t^{4} cos (14 t) + 1372 t^{3} sin (14 t) - 3 (- 98 t^{2} cos (14 t) + 14 t sin (14 t) + cos (14 t)))) cos (7 t) + \frac{1}{67228} (- 1372 t^{3} cos (14 t) + 3 (98 t^{2} sin (14 t) + 14 t cos (14 t) - sin (14 t))) sin (7 t)

Solution steps

y^{''} (t) + 49 y = 4 t^{3} sin (7 t)

Solve linear ODE:

y = c_{1} cos (7 t) + c_{2} sin (7 t) + (- \frac{1}{7} t^{4} sin^{2} (7 t) + \frac{1}{67228} (- 4802 t^{4} cos (14 t) + 1372 t^{3} sin (14 t) - 3 (- 98 t^{2} cos (14 t) + 14 t sin (14 t) + cos (14 t)))) cos (7 t) + \frac{1}{67228} (- 1372 t^{3} cos (14 t) + 3 (98 t^{2} sin (14 t) + 14 t cos (14 t) - sin (14 t))) sin (7 t)

y = c_{1} cos (7 t) + c_{2} sin (7 t) + (- \frac{1}{7} t^{4} sin^{2} (7 t) + \frac{1}{67228} (- 4802 t^{4} cos (14 t) + 1372 t^{3} sin (14 t) - 3 (- 98 t^{2} cos (14 t) + 14 t sin (14 t) + cos (14 t)))) cos (7 t) + \frac{1}{67228} (- 1372 t^{3} cos (14 t) + 3 (98 t^{2} sin (14 t) + 14 t cos (14 t) - sin (14 t))) sin (7 t)

Graph

Popular Examples

(D^2+1)y=sec(xtan(x))

(D^{2} + 1) y = sec (x tan (x))

4x^{''}+kx=8sin(t)

4 x^{^{''}} + k x = 8 sin (t)

y^{''}-2y^'+y=x^2-2-2cos(x)

y^{^{''}} - 2 y^{^{'}} + y = x^{2} - 2 - 2 cos (x)

y^{''}+4y= 5/2 cos(2t)

y^{^{''}} + 4 y = \frac{5}{2} cos (2 t)

y^{''}+4y=e^{3t}+4cos(3t)

y^{^{''}} + 4 y = e^{3 t} + 4 cos (3 t)

Frequently Asked Questions (FAQ)

What is the solution for y^{''}+49y=4t^3sin(7t) ?
The solution for y^{''}+49y=4t^3sin(7t) is