27.8 problem Ex 8

Internal problem ID [10256]

Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section: Chapter VII, Linear differential equations with constant coefficients. Article 50. Method of undetermined coefficients. Page 107
Problem number: Ex 8.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _missing_y]]

Solve \begin {gather*} \boxed {y^{\prime \prime }-2 y^{\prime }-{\mathrm e}^{2 x}-1=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 29

dsolve(diff(y(x),x$2)-2*diff(y(x),x)=exp(2*x)+1,y(x), singsol=all)
 

\[ y \relax (x ) = -\frac {x}{2}+\frac {x \,{\mathrm e}^{2 x}}{2}-\frac {{\mathrm e}^{2 x}}{4}+\frac {{\mathrm e}^{2 x} c_{1}}{2}+c_{2} \]

Solution by Mathematica

Time used: 0.098 (sec). Leaf size: 31

DSolve[y''[x]-2*y'[x]==Exp[2*x]+1,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {x}{2}+\frac {1}{4} e^{2 x} (2 x-1+2 c_1)+c_2 \\ \end{align*}