Internal problem ID [4745]
Book: Advanced Mathemtical Methods for Scientists and Engineers, Bender and Orszag. Springer
October 29, 1999
Section: Chapter 3. APPROXIMATE SOLUTION OF LINEAR DIFFERENTIAL EQUATIONS. page
136
Problem number: 3.48 (b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }+x y-\frac {1}{x^{3}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(diff(y(x),x)+x*y(x)=1/x^3,y(x), singsol=all)
\[ y \left (x \right ) = \left (-\frac {{\mathrm e}^{\frac {x^{2}}{2}}}{2 x^{2}}-\frac {\operatorname {Ei}_{1}\left (-\frac {x^{2}}{2}\right )}{4}+c_{1} \right ) {\mathrm e}^{-\frac {x^{2}}{2}} \]
✓ Solution by Mathematica
Time used: 0.061 (sec). Leaf size: 38
DSolve[y'[x]+x*y[x]==1/x^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} \left (-\frac {2}{x^2}+e^{-\frac {x^2}{2}} \left (\operatorname {ExpIntegralEi}\left (\frac {x^2}{2}\right )+4 c_1\right )\right ) \\ \end{align*}