Internal problem ID [5505]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime } x^{2}-2 y-3 x^{2}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.11 (sec). Leaf size: 39
dsolve([x^2*diff(y(x),x)-2*y(x)=3*x^2,y(1) = 2],y(x), singsol=all)
\[ y \relax (x ) = \left (-6 \expIntegral \left (1, -2\right )+6 \expIntegral \left (1, -\frac {2}{x}\right )\right ) {\mathrm e}^{-\frac {2}{x}}+3 x -{\mathrm e}^{2-\frac {2}{x}} \]
✓ Solution by Mathematica
Time used: 0.059 (sec). Leaf size: 34
DSolve[{x^2*y'[x]-2*y[x]==3*x^2,{y[1]==2}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 3 x-e^{-2/x} \left (6 \text {Ei}\left (\frac {2}{x}\right )-6 \text {Ei}(2)+e^2\right ) \\ \end{align*}