Internal problem ID [2217]
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: 16.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y=x \,{\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(y(x),x$2)+4*y(x)=x*exp(x),y(x), singsol=all)
\[ y = c_{2} \sin \left (2 x \right )+\cos \left (2 x \right ) c_{1} +\frac {\left (5 x -2\right ) {\mathrm e}^{x}}{25} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 32
DSolve[y''[x]+4*y[x]==x*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{25} e^x (5 x-2)+c_1 \cos (2 x)+c_2 \sin (2 x) \]