62.30.8 problem Ex 8

Internal problem ID [12972]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter VIII, Linear differential equations of the second order. Article 53. Change of dependent variable. Page 125
Problem number : Ex 8
Date solved : Tuesday, January 28, 2025 at 04:45:54 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 21

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

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

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 35

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

\[ y(x)\to \frac {e^{-x} \left (e^{2 x} (2 x-1+c_2)+2 c_1\right )}{2 x} \]