15.12.4 problem 4

Internal problem ID [3148]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 20, page 90
Problem number : 4
Date solved : Monday, January 27, 2025 at 07:23:42 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

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

\[ y = {\mathrm e}^{2 x}+\left (c_{1} x +c_2 \right ) {\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 19

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

\[ y(x)\to e^x \left (e^x+c_2 x+c_1\right ) \]