Internal problem ID [11845]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.4. Variation of parameters. Exercises page 162
Problem number: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+3 y^{\prime }+2 y=\frac {{\mathrm e}^{-x}}{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(diff(y(x),x$2)+3*diff(y(x),x)+2*y(x)=exp(-x)/x,y(x), singsol=all)
\[ y \left (x \right ) = \left (-\left (\int {\mathrm e}^{-x} \left (\operatorname {expIntegral}_{1}\left (-x \right )-c_{1} \right )d x \right )+c_{2} \right ) {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.041 (sec). Leaf size: 30
DSolve[y''[x]+3*y'[x]+2*y[x]==Exp[-x]/x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-2 x} \left (-\operatorname {ExpIntegralEi}(x)+e^x \log (x)+c_2 e^x+c_1\right ) \]