73.15.19 problem 22.7 (d)

Internal problem ID [15450]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 22. Method of undetermined coefficients. Additional exercises page 412
Problem number : 22.7 (d)
Date solved : Tuesday, January 28, 2025 at 07:56:16 AM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} y^{\prime \prime }&=6 x \,{\mathrm e}^{x} \sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 25

dsolve(diff(y(x),x$2)=6*x*exp(x)*sin(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.045 (sec). Leaf size: 38

DSolve[D[y[x],{x,2}]==6*x*Exp[x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _1^x\int _1^{K[2]}6 e^{K[1]} K[1] \sin (K[1])dK[1]dK[2]+c_2 x+c_1 \]