75.16.71 problem 544

Internal problem ID [17044]
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 ODEs). Section 15.3 Nonhomogeneous linear equations with constant coefficients. Trial and error method. Exercises page 132
Problem number : 544
Date solved : Tuesday, January 28, 2025 at 09:47:26 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=x^{2} \sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 33

dsolve(diff(y(x),x$2)+y(x)=x^2*sin(x),y(x), singsol=all)
 

\[ y = \frac {\left (-2 x^{3}+12 c_{1} +3 x \right ) \cos \left (x \right )}{12}+\frac {\sin \left (x \right ) \left (x^{2}+4 c_{2} -1\right )}{4} \]

✓ Solution by Mathematica

Time used: 0.104 (sec). Leaf size: 58

DSolve[D[y[x],{x,2}]+y[x]==x^2*Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \cos (x) \int _1^x-K[1]^2 \sin ^2(K[1])dK[1]+\sin (x) \int _1^x\cos (K[2]) K[2]^2 \sin (K[2])dK[2]+c_1 \cos (x)+c_2 \sin (x) \]