Internal problem ID [170]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.1, second order linear equations. Page 299
Problem number: 14.
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 -6 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (2) = 10, y^{\prime }\relax (2) = 15] \end {align*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 15
dsolve([x^2*diff(y(x),x$2)+2*x*diff(y(x),x)-6*y(x)=0,y(2) = 10, D(y)(2) = 15],y(x), singsol=all)
\[ y \relax (x ) = \frac {3 x^{5}-16}{x^{3}} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 16
DSolve[{x^2*y''[x]+2*x*y'[x]-6*y[x]==0,{y[2]==10,y'[2]==15}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {3 x^5-16}{x^3} \\ \end{align*}