Internal problem ID [15334]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 15.3 Nonhomogeneous linear equations with
constant coefficients. Superposition principle. Exercises page 137
Problem number: 565.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y=x \sin \left (x \right )^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
dsolve(diff(y(x),x$2)+4*y(x)=x*sin(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (-8 x^{2}+128 c_{2} +1\right ) \sin \left (2 x \right )}{128}+\frac {\left (-x +32 c_{1} \right ) \cos \left (2 x \right )}{32}+\frac {x}{8} \]
✓ Solution by Mathematica
Time used: 0.245 (sec). Leaf size: 41
DSolve[y''[x]+4*y[x]==x*Sin[x]^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{128} \left (\left (-8 x^2+1+128 c_2\right ) \sin (2 x)+16 x-4 (x-32 c_1) \cos (2 x)\right ) \]