82.49.1 problem Ex. 1

Internal problem ID [19003]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter IX. Equations of the second order. problems at page 111
Problem number : Ex. 1
Date solved : Tuesday, January 28, 2025 at 12:45:09 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y&={\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 16

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

\[ y \left (x \right ) = {\mathrm e}^{x} \left (c_{1} \operatorname {Ei}_{1}\left (x \right )+\ln \left (x \right )+c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.072 (sec). Leaf size: 23

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

\[ y(x)\to e^x (c_2 \operatorname {ExpIntegralEi}(-x)+\log (-x)+c_1) \]