Internal problem ID [4635]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 22. Variation of
Parameters
Problem number: Exercise 22.5, page 240.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=\sin \left (x \right )^{2}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
dsolve(diff(y(x),x$2)+y(x)=sin(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = c_{2} \sin \left (x \right )+c_{1} \cos \left (x \right )+\frac {1}{2}+\frac {\cos \left (2 x \right )}{6} \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 27
DSolve[y''[x]+y[x]==Sin[x]^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{6} (\cos (2 x)+6 c_1 \cos (x)+6 c_2 \sin (x)+3) \]