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Popular Calculus >

(d^2+9)y=30sin^3(x)

Solution

(d^{2} + 9) y = 30 sin^{3} (x)

Solution

y = c_{1} cos (3 x) + c_{2} sin (3 x) - 10 cos (3 x) (- sin (3 x) cos (x) + \frac{1}{3} cos^{3} (x) sin (3 x) - \frac{1}{8} x + \frac{13}{32} sin (4 x) + \frac{23}{32} sin (2 x) - \frac{1}{8} cos^{2} (x) sin (4 x) - \frac{1}{4} cos^{2} (x) sin (2 x) + \frac{1}{96} sin (6 x)) + sin (3 x) \cdot \int 10 sin^{3} (x) cos (3 x) d x

Solution steps

(d^{2} + 9) y = 30 sin^{3} (x)

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) - 10 cos (3 x) (- sin (3 x) cos (x) + \frac{1}{3} cos^{3} (x) sin (3 x) - \frac{1}{8} x + \frac{13}{32} sin (4 x) + \frac{23}{32} sin (2 x) - \frac{1}{8} cos^{2} (x) sin (4 x) - \frac{1}{4} cos^{2} (x) sin (2 x) + \frac{1}{96} sin (6 x)) + sin (3 x) \cdot \int 10 sin^{3} (x) cos (3 x) d x

y = c_{1} cos (3 x) + c_{2} sin (3 x) - 10 cos (3 x) (- sin (3 x) cos (x) + \frac{1}{3} cos^{3} (x) sin (3 x) - \frac{1}{8} x + \frac{13}{32} sin (4 x) + \frac{23}{32} sin (2 x) - \frac{1}{8} cos^{2} (x) sin (4 x) - \frac{1}{4} cos^{2} (x) sin (2 x) + \frac{1}{96} sin (6 x)) + sin (3 x) \cdot \int 10 sin^{3} (x) cos (3 x) d x

Popular Examples

y^{''''}-y=11t+cos(t)

y^{''}-4y^'+4y=10e^{2x}

2(d^2y)/(dx^2)-5(dy)/(dx)-3=0

(d^3-3d^2+4d-2)y=x^3

y^{''}=2y+tan^3(x),y(0)= 1/2 tan(x)

Frequently Asked Questions (FAQ)

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