62.27.8 problem Ex 8

Internal problem ID [12946]
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
Date solved : Tuesday, January 28, 2025 at 04:44:46 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }&={\mathrm e}^{2 x}+1 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 23

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

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

✓ Solution by Mathematica

Time used: 1.784 (sec). Leaf size: 64

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

\begin{align*} y(x)\to \int _1^x\left (e^{2 K[1]} (c_1+K[1])-\frac {1}{2}\right )dK[1]+c_2 \\ y(x)\to \frac {1}{4} \left (-2 x+e^{2 x} (2 x-1)-e^2+2+4 c_2\right ) \\ \end{align*}