50.8.2 problem 1(b)

Internal problem ID [7918]
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)
Date solved : Monday, January 27, 2025 at 03:32:16 PM
CAS classification : [_linear]

\begin{align*} x^{2} y^{\prime }+y&=x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 23

dsolve(x^2*diff(y(x),x)+y(x)=x^2,y(x), singsol=all)
 

\[ y = x -{\mathrm e}^{\frac {1}{x}} \operatorname {Ei}_{1}\left (\frac {1}{x}\right )+{\mathrm e}^{\frac {1}{x}} c_{1} \]

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 27

DSolve[x^2*D[y[x],x]+y[x]==x^2,y[x],x,IncludeSingularSolutions -> True]
 

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