Internal problem ID [4116]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 21. Undetermined
Coefficients
Problem number: Exercise 21.24, page 231.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y-\left (\sin ^{2}\relax (x )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 20
dsolve(diff(y(x),x$2)+y(x)=sin(x)^2,y(x), singsol=all)
\[ y \relax (x ) = c_{2} \sin \relax (x )+\cos \relax (x ) c_{1}+\frac {1}{2}+\frac {\cos \left (2 x \right )}{6} \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 27
DSolve[y''[x]+y[x]==Sin[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} (\cos (2 x)+6 c_1 \cos (x)+6 c_2 \sin (x)+3) \\ \end{align*}