Differential Equations Quiz
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SECOND-ORDER LINEAR ODES
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The differential equation y′′+y=cos⁡(x)+xsin⁡(x)y'' + y = \cos(x) + x\sin(x) has homogeneous solution yh=c1cos⁡(x)+c2sin⁡(x)y_h = c_1\cos(x) + c_2\sin(x). If yp1=12xsin⁡(x)y_{p1} = \frac{1}{2}x\sin(x) is a particular solution to y′′+y=cos⁡(x)y'' + y = \cos(x) and yp2=−14x2cos⁡(x)y_{p2} = -\frac{1}{4}x^2\cos(x) is a particular solution to y′′+y=xsin⁡(x)y'' + y = x\sin(x), which analysis of the complete particular solution is correct?
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