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Popular >

(d^2+9)y=cos^2(x)

Solution

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

Solution

y = c_{1} cos (3 x) + c_{2} sin (3 x) - \frac{1}{6} cos (3 x) (- \frac{1}{3} cos (3 x) + \frac{1}{2} (- \frac{1}{5} cos (5 x) - cos (x))) + \frac{1}{3} sin (3 x) (\frac{1}{3} cos^{2} (x) sin (3 x) + \frac{1}{6} (sin (x) - \frac{1}{5} sin (5 x)))

Solution steps

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

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) - \frac{1}{6} cos (3 x) (- \frac{1}{3} cos (3 x) + \frac{1}{2} (- \frac{1}{5} cos (5 x) - cos (x))) + \frac{1}{3} sin (3 x) (\frac{1}{3} cos^{2} (x) sin (3 x) + \frac{1}{6} (sin (x) - \frac{1}{5} sin (5 x)))

y = c_{1} cos (3 x) + c_{2} sin (3 x) - \frac{1}{6} cos (3 x) (- \frac{1}{3} cos (3 x) + \frac{1}{2} (- \frac{1}{5} cos (5 x) - cos (x))) + \frac{1}{3} sin (3 x) (\frac{1}{3} cos^{2} (x) sin (3 x) + \frac{1}{6} (sin (x) - \frac{1}{5} sin (5 x)))

Graph

Popular Examples

(d^4-1)*y=sin(x)

(d^{4} - 1) \cdot y = sin (x)

(d^2-4)y=xsinh(x)

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

(d^2-4d-6)y=e^2x

(d^{2} - 4 d - 6) y = e^{2} x

(d^3-6d^2+11d-6)y=e^{-2}x+e^2x

(d^{3} - 6 d^{2} + 11 d - 6) y = e^{- 2} x + e^{2} x

(d^3-d^2+d-1)y=4sin(x)

(d^{3} - d^{2} + d - 1) y = 4 sin (x)

Frequently Asked Questions (FAQ)

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