12.10.8 problem 8

Internal problem ID [1812]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 5 linear second order equations. Section 5.7 Variation of Parameters. Page 262
Problem number : 8
Date solved : Monday, January 27, 2025 at 05:35:48 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 17

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

\[ y = \frac {{\mathrm e}^{x} \left (c_2 x +{\mathrm e}^{x}+c_1 \right )}{x} \]

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 22

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

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