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Popular >

(d^4+d^2+16)y=16x^2+256

Solution

(d^{4} + d^{2} + 16) y = 16 x^{2} + 256

Solution

y = e^{\frac{7 x}{2}} (c_{1} cos (\frac{3 x}{2}) + c_{2} sin (\frac{3 x}{2})) + e^{- \frac{7 x}{2}} (c_{3} cos (\frac{3 x}{2}) + c_{4} sin (\frac{3 x}{2})) + x^{2} + \frac{127}{8}

Solution steps

(d^{4} + d^{2} + 16) y = 16 x^{2} + 256

Solve linear ODE:

y = e^{\frac{7 x}{2}} (c_{1} cos (\frac{3 x}{2}) + c_{2} sin (\frac{3 x}{2})) + e^{- \frac{7 x}{2}} (c_{3} cos (\frac{3 x}{2}) + c_{4} sin (\frac{3 x}{2})) + x^{2} + \frac{127}{8}

y = e^{\frac{7 x}{2}} (c_{1} cos (\frac{3 x}{2}) + c_{2} sin (\frac{3 x}{2})) + e^{- \frac{7 x}{2}} (c_{3} cos (\frac{3 x}{2}) + c_{4} sin (\frac{3 x}{2})) + x^{2} + \frac{127}{8}

Popular Examples

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y^{^{''}} + 10 y^{^{'}} + 25 y = e^{- 5} x

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y^{^{''}} + 3 y^{^{'}} + 2 y = 12 e^{x}

solvefor y,(d^3-d)y=2cos(t)solve for

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

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

Frequently Asked Questions (FAQ)

What is the solution for (d^4+d^2+16)y=16x^2+256 ?
The solution for (d^4+d^2+16)y=16x^2+256 is