Internal problem ID [13714]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _quadrature]]
\[ \boxed {y^{\prime \prime }=6 x \,{\mathrm e}^{x} \sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(diff(y(x),x$2)=6*x*exp(x)*sin(x),y(x), singsol=all)
\[ y \left (x \right ) = \left (\left (-3 x +3\right ) \cos \left (x \right )+3 \sin \left (x \right )\right ) {\mathrm e}^{x}+c_{1} x +c_{2} \]
✓ Solution by Mathematica
Time used: 0.104 (sec). Leaf size: 27
DSolve[y''[x]==6*x*Exp[x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 x+3 e^x (\sin (x)-x \cos (x)+\cos (x))+c_1 \]