Internal problem ID [10252]
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]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }-{\mathrm e}^{2 x}-1=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(diff(y(x),x$2)-2*diff(y(x),x)=exp(2*x)+1,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {x}{2}+\frac {{\mathrm e}^{2 x} x}{2}-\frac {{\mathrm e}^{2 x}}{4}+\frac {{\mathrm e}^{2 x} c_{1}}{2}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.08 (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*}