50.8.10 problem 2(b)

Internal problem ID [7926]
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 : 2(b)
Date solved : Monday, January 27, 2025 at 03:32:40 PM
CAS classification : [_linear]

\begin{align*} x^{2} y^{\prime }-2 y&=3 x^{2} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.113 (sec). Leaf size: 44

dsolve([x^2*diff(y(x),x)-2*y(x)=3*x^2,y(1) = 2],y(x), singsol=all)
 

\[ y = 3 x -{\mathrm e}^{2-\frac {2}{x}}+6 \,\operatorname {Ei}_{1}\left (-\frac {2}{x}\right ) {\mathrm e}^{-\frac {2}{x}}-6 \,\operatorname {Ei}_{1}\left (-2\right ) {\mathrm e}^{-\frac {2}{x}} \]

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 41

DSolve[{x^2*D[y[x],x]-2*y[x]==3*x^2,{y[1]==2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2/x} \left (-6 \operatorname {ExpIntegralEi}\left (\frac {2}{x}\right )+6 \operatorname {ExpIntegralEi}(2)+3 e^{2/x} x-e^2\right ) \]