Internal problem ID [5499]
Book: Advanced Mathematical 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]
\[ \boxed {y^{\prime }+x y=\frac {1}{x^{3}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 41
dsolve(diff(y(x),x)+x*y(x)=1/x^3,y(x), singsol=all)
\[ y \left (x \right ) = \frac {4 c_{1} x^{2} {\mathrm e}^{-\frac {x^{2}}{2}}-\operatorname {expIntegral}_{1}\left (-\frac {x^{2}}{2}\right ) x^{2} {\mathrm e}^{-\frac {x^{2}}{2}}-2}{4 x^{2}} \]
✓ Solution by Mathematica
Time used: 0.067 (sec). Leaf size: 46
DSolve[y'[x]+x*y[x]==1/x^3,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} e^{-\frac {x^2}{2}} \operatorname {ExpIntegralEi}\left (\frac {x^2}{2}\right )-\frac {1}{2 x^2}+c_1 e^{-\frac {x^2}{2}} \]