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Popular >

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

Solution

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

Solution

y = c_{1} cos (3 x) + c_{2} sin (3 x) - \frac{1}{3} 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 \frac{sin ^{3} ( x ) cos ( 3 x )}{3} d x

Solution steps

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

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) - \frac{1}{3} 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 \frac{sin ^{3} ( x ) cos ( 3 x )}{3} d x

y = c_{1} cos (3 x) + c_{2} sin (3 x) - \frac{1}{3} 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 \frac{sin ^{3} ( x ) cos ( 3 x )}{3} d x

Popular Examples

(d^2+2)y=e^x*cos^3(x)

(d^{2} + 2) y = e^{x} \cdot cos^{3} (x)

[d^2-d-12]*y=e^{3x}

[d^{2} - d - 12] \cdot y = e^{3 x}

y^{''}-2y^'=sin(2x)

y^{^{''}} - 2 y^{^{'}} = sin (2 x)

(d)h(x)= 1/((1+x^2))

(d) h (x) = \frac{1}{( 1 + x ^{2} )}

(d^2+3d+1)*y=x^2*e^{3x}

(d^{2} + 3 d + 1) \cdot y = x^{2} \cdot e^{3 x}

Frequently Asked Questions (FAQ)

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