Internal problem ID [5496]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Problems for Review and Discovery. Page
53
Problem number: 1(b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {x^{2} y^{\prime }+y-x^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(x^2*diff(y(x),x)+y(x)=x^2,y(x), singsol=all)
\[ y \left (x \right ) = x -\operatorname {Ei}_{1}\left (\frac {1}{x}\right ) {\mathrm e}^{\frac {1}{x}}+{\mathrm e}^{\frac {1}{x}} c_{1} \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 22
DSolve[x^2*y'[x]+y[x]==x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x+e^{\frac {1}{x}} \left (\operatorname {ExpIntegralEi}\left (-\frac {1}{x}\right )+c_1\right ) \\ \end{align*}