Internal problem ID [2218]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 23, page 106
Problem number: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+2 y=x^{2} {\mathrm e}^{-x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 35
dsolve(diff(y(x),x$2)+2*y(x)=x^2*exp(-x),y(x), singsol=all)
\[ y \left (x \right ) = \cos \left (\sqrt {2}\, x \right ) c_{1} +c_{2} \sin \left (\sqrt {2}\, x \right )+\frac {\left (x^{2}+\frac {4}{3} x +\frac {2}{9}\right ) {\mathrm e}^{-x}}{3} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 47
DSolve[y''[x]+2*y[x]==x^2*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{27} e^{-x} \left (9 x^2+12 x+2\right )+c_1 \cos \left (\sqrt {2} x\right )+c_2 \sin \left (\sqrt {2} x\right ) \]