42.1.20 problem 3.48 (b)

Internal problem ID [6842]
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)
Date solved : Monday, January 27, 2025 at 02:31:33 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }+y x&=\frac {1}{x^{3}} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 41

dsolve(diff(y(x),x)+x*y(x)=1/x^3,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.102 (sec). Leaf size: 46

DSolve[D[y[x],x]+x*y[x]==1/x^3,y[x],x,IncludeSingularSolutions -> True]
 

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