Internal problem ID [2249]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 24, page 109
Problem number: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }=x^{2} {\mathrm e}^{-x} \sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 41
dsolve(diff(y(x),x$2)+2*diff(y(x),x)=x^2*exp(-x)*sin(x),y(x), singsol=all)
\[ y = -\frac {x^{2} \sin \left (x \right ) {\mathrm e}^{-x}}{2}+\frac {{\mathrm e}^{-x} \sin \left (x \right )}{2}-x \,{\mathrm e}^{-x} \cos \left (x \right )-\frac {c_{1} {\mathrm e}^{-2 x}}{2}+c_{2} \]
✓ Solution by Mathematica
Time used: 1.508 (sec). Leaf size: 39
DSolve[y''[x]+2*y'[x]==x^2*Exp[-x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2-\frac {1}{2} e^{-2 x} \left (e^x \left (x^2-1\right ) \sin (x)+2 e^x x \cos (x)+c_1\right ) \]