Internal problem ID [2180]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 20, page 90
Problem number: 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-y=3 x +5 \,{\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(y(x),x$2)-y(x)=3*x+5*exp(x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-x} c_{2} +\frac {\left (10 x +4 c_{1} -5\right ) {\mathrm e}^{x}}{4}-3 x \]
✓ Solution by Mathematica
Time used: 0.095 (sec). Leaf size: 32
DSolve[y''[x]-y[x]==3*x+5*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -3 x+e^x \left (\frac {5 x}{2}-\frac {5}{4}+c_1\right )+c_2 e^{-x} \]