Internal problem ID [2142]
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: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+y^{\prime }-2 y={\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(diff(y(x),x$2)+diff(y(x),x)-2*y(x)=exp(x),y(x), singsol=all)
\[ y = {\mathrm e}^{-2 x} c_{2} +c_{1} {\mathrm e}^{x}+\frac {x \,{\mathrm e}^{x}}{3} \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 29
DSolve[y''[x]+y'[x]-2*y[x]==Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^{-2 x}+e^x \left (\frac {x}{3}-\frac {1}{9}+c_2\right ) \]