Internal problem ID [10269]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter VII, Linear differential equations with constant coefficients. Article 52. Summary.
Page 117
Problem number: Ex 9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+4 y-\left (\sin ^{2}\relax (x )\right )=0} \end {gather*}
✓ 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)
\[ y \relax (x ) = \sin \left (2 x \right ) c_{2}+\cos \left (2 x \right ) c_{1}-\frac {\sin \left (2 x \right ) x}{8}+\frac {1}{8}-\frac {\cos \left (2 x \right )}{8} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 34
DSolve[y''[x]+4*y[x]==Sin[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{8} ((-1+8 c_1) \cos (2 x)-(x-8 c_2) \sin (2 x)+1) \\ \end{align*}