Internal problem ID [2148]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 19, page 86
Problem number: 9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-4 y=x +{\mathrm e}^{2 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve(diff(y(x),x$2)-4*y(x)=x+exp(2*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (4 x +16 c_{2} -1\right ) {\mathrm e}^{2 x}}{16}+{\mathrm e}^{-2 x} c_{1} -\frac {x}{4} \]
✓ Solution by Mathematica
Time used: 0.082 (sec). Leaf size: 36
DSolve[y''[x]-4*y[x]==x+Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {x}{4}+e^{2 x} \left (\frac {x}{4}-\frac {1}{16}+c_1\right )+c_2 e^{-2 x} \]