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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

xy^{''}+xy^'=x^3

x y^{^{''}} + x y^{^{'}} = x^{3}

y^{''}-y^'-6y=8cos(3x)

y^{^{''}} - y^{^{'}} - 6 y = 8 cos (3 x)

y^{''}+60y^'+900y=-360xe^{-4x}

y^{^{''}} + 60 y^{^{'}} + 900 y = - 360 x e^{- 4 x}

y^{''}-8y^'+16y=e^4x

y^{^{''}} - 8 y^{^{'}} + 16 y = e^{4} x

y^{''}-y=12x^2+e^x

y^{^{''}} - y = 12 x^{2} + e^{x}

Frequently Asked Questions (FAQ)

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