Internal problem ID [8643]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1063.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-\left (2 \,{\mathrm e}^{x}+1\right ) y^{\prime }+y \,{\mathrm e}^{2 x}-{\mathrm e}^{3 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.011 (sec). Leaf size: 34
dsolve(diff(diff(y(x),x),x)-(2*exp(x)+1)*diff(y(x),x)+exp(2*x)*y(x)-exp(3*x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\frac {x}{2}+{\mathrm e}^{x}} \sinh \left (\frac {x}{2}\right ) c_{2}+{\mathrm e}^{\frac {x}{2}+{\mathrm e}^{x}} \cosh \left (\frac {x}{2}\right ) c_{1}+{\mathrm e}^{x}+2 \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 28
DSolve[-E^(3*x) + E^(2*x)*y[x] - (1 + 2*E^x)*y'[x] + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x+c_1 e^{e^x}+c_2 e^{x+e^x}+2 \\ \end{align*}