Internal problem ID [169]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.1, second order linear equations. Page 299
Problem number: 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, _with_symmetry_[0,F(x)]]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 3, y^{\prime }\relax (1) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 13
dsolve([x^2*diff(y(x),x$2)-2*x*diff(y(x),x)+2*y(x)=0,y(1) = 3, D(y)(1) = 1],y(x), singsol=all)
\[ y \relax (x ) = -2 x^{2}+5 x \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 12
DSolve[{x^2*y''[x]-2*x*y'[x]+2*y[x]==0,{y[1]==3,y'[1]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to (5-2 x) x \\ \end{align*}