Internal problem ID [171]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.1, second order linear equations. Page 299
Problem number: 15.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-y^{\prime } x +y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 7, y^{\prime }\relax (1) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 13
dsolve([x^2*diff(y(x),x$2)-x*diff(y(x),x)+y(x)=0,y(1) = 7, D(y)(1) = 2],y(x), singsol=all)
\[ y \relax (x ) = 7 x -5 x \ln \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 13
DSolve[{x^2*y''[x]-x*y'[x]+y[x]==0,{y[1]==7,y'[1]==2}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x (7-5 \log (x)) \\ \end{align*}