Internal problem ID [5300]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {-3 y+y^{\prime } x=\left (x -2\right ) {\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 38
dsolve((-2*y(x)-(x-2)*exp(x))+x*diff(y(x),x)-y(x)=0,y(x), singsol=all)
\[ y = \left (-\frac {{\mathrm e}^{x}}{6 x^{2}}-\frac {{\mathrm e}^{x}}{6 x}-\frac {\operatorname {Ei}_{1}\left (-x \right )}{6}+\frac {2 \,{\mathrm e}^{x}}{3 x^{3}}+c_{1} \right ) x^{3} \]
✓ Solution by Mathematica
Time used: 0.109 (sec). Leaf size: 33
DSolve[(-2*y[x]-(x-2)*Exp[x])+x*y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{6} x^3 \left (\operatorname {ExpIntegralEi}(x)-\frac {e^x \left (x^2+x-4\right )}{x^3}+6 c_1\right ) \]