Internal problem ID [15314]
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. Trial and error method. Exercises page 132
Problem number: 544.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=x^{2} \sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 33
dsolve(diff(y(x),x$2)+y(x)=x^2*sin(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (-2 x^{3}+12 c_{1} +3 x \right ) \cos \left (x \right )}{12}+\frac {\sin \left (x \right ) \left (x^{2}+4 c_{2} -1\right )}{4} \]
✓ Solution by Mathematica
Time used: 0.102 (sec). Leaf size: 41
DSolve[y''[x]+y[x]==x^2*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \left (-\frac {x^3}{6}+\frac {x}{4}+c_1\right ) \cos (x)+\frac {1}{8} \left (2 x^2-1+8 c_2\right ) \sin (x) \]