Internal problem ID [8614]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1034.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, _with_symmetry_[0,F(x)]]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-y^{\prime }+y \,{\mathrm e}^{2 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 15
dsolve(diff(diff(y(x),x),x)-diff(y(x),x)+exp(2*x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sin \left ({\mathrm e}^{x}\right )+c_{2} \cos \left ({\mathrm e}^{x}\right ) \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 20
DSolve[E^(2*x)*y[x] - y'[x] + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \cos \left (e^x\right )+c_2 \sin \left (e^x\right ) \\ \end{align*}