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Popular >

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

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

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

y^{''}-2y^'+3=e^t,y(0)=1,y^'(0)=2

y^{^{''}} - 2 y^{^{'}} + 3 = e^{t}, y (0) = 1, y^{^{'}} (0) = 2

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

2 \frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} - 3 = 0

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

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

Frequently Asked Questions (FAQ)

What is the solution for (d^2+9)y=30sin^3(x) ?
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