Internal problem ID [250]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page
351
Problem number: 55.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y=\sin \left (x \right )^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(diff(y(x),x$2)+4*y(x)=sin(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (2 x \right ) c_{2} +\cos \left (2 x \right ) c_{1} -\frac {\sin \left (2 x \right ) x}{8}+\frac {1}{8}-\frac {\cos \left (2 x \right )}{8} \]
✓ Solution by Mathematica
Time used: 0.111 (sec). Leaf size: 71
DSolve[y''[x]+4*y[x]==sin[x]^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \cos (2 x) \int _1^x-\cos (K[1]) \sin (K[1])^2 \sin (K[1])dK[1]+\sin (2 x) \int _1^x\frac {1}{2} \cos (2 K[2]) \sin (K[2])^2dK[2]+c_1 \cos (2 x)+c_2 \sin (2 x) \]