Can someone show how to solve: y'' + 9y = sin^4(x)
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First find the charateristic equation to the homogeneous equation and solve it. y'' + 9y = 0 gives r^2 + 9 = 0 Now solve this guy, you should get complex solutions. What does this mean?
Got that. yc(x) = c1cos3x + c2sin3x I get duplication tho right? what do I do from here?
Originally Posted by jzellt Got that. yc(x) = c1cos3x + c2sin3x I get duplication tho right? what do I do from here? To get a particular solution, note (using the usual double angle formulae) that $\displaystyle \displaystyle \sin^4 (x) = -\frac{1}{2} \cos (2x) + \frac{1}{8} \cos (4x) + \frac{3}{8}$.
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