Internal problem ID [172]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.1, second order linear equations. Page 299
Problem number: 16.
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 }+y^{\prime } x +y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 2, y^{\prime }\relax (1) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 15
dsolve([x^2*diff(y(x),x$2)+x*diff(y(x),x)+y(x)=0,y(1) = 2, D(y)(1) = 3],y(x), singsol=all)
\[ y \relax (x ) = 3 \sin \left (\ln \relax (x )\right )+2 \cos \left (\ln \relax (x )\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 16
DSolve[{x^2*y''[x]+x*y'[x]+y[x]==0,{y[1]==2,y'[1]==3}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 3 \sin (\log (x))+2 \cos (\log (x)) \\ \end{align*}