Internal problem ID [2205]
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: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+y^{\prime }-2 y={\mathrm e}^{-2 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve(diff(y(x),x$2)+diff(y(x),x)-2*y(x)=exp(-2*x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\left (-3 c_{1} {\mathrm e}^{3 x}-3 c_{2} +x \right ) {\mathrm e}^{-2 x}}{3} \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 32
DSolve[y''[x]+y'[x]-2*y[x]==Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{9} e^{-2 x} \left (-3 x+9 c_2 e^{3 x}-1+9 c_1\right ) \]