Internal problem ID [10243]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter VII, Linear differential equations with constant coefficients. Article 48. Page
103
Problem number: Ex 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-3 y^{\prime }+2 y-{\mathrm e}^{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(diff(y(x),x$2)-3*diff(y(x),x)+2*y(x)=exp(x),y(x), singsol=all)
\[ y \relax (x ) = \left (-x +c_{1} {\mathrm e}^{x}+c_{2}\right ) {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 22
DSolve[y''[x]-3*y'[x]+2*y[x]==Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x \left (-x+c_2 e^x-1+c_1\right ) \\ \end{align*}