40.4.3 problem 19 (d)

Internal problem ID [6643]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 6. Equations of first order and first degree (Linear equations). Supplemetary problems. Page 39
Problem number : 19 (d)
Date solved : Monday, January 27, 2025 at 02:16:35 PM
CAS classification : [_linear]

\begin{align*} -3 y-\left (x -2\right ) {\mathrm e}^{x}+x y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 34

dsolve((-2*y(x)-(x-2)*exp(x))+x*diff(y(x),x)-y(x)=0,y(x), singsol=all)
 

\[ y = -\frac {x^{3} \operatorname {Ei}_{1}\left (-x \right )}{6}+\frac {\left (-x^{2}-x +4\right ) {\mathrm e}^{x}}{6}+c_1 \,x^{3} \]

✓ Solution by Mathematica

Time used: 0.145 (sec). Leaf size: 33

DSolve[(-2*y[x]-(x-2)*Exp[x])+x*D[y[x],x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{6} x^3 \left (\operatorname {ExpIntegralEi}(x)-\frac {e^x \left (x^2+x-4\right )}{x^3}+6 c_1\right ) \]