Internal problem ID [185]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.1, second order linear equations. Page 299
Problem number: 54.
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 {4 x^{2} y^{\prime \prime }+8 y^{\prime } x -3 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 15
dsolve(4*x^2*diff(y(x),x$2)+8*x*diff(y(x),x)-3*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sqrt {x}+\frac {c_{2}}{x^{\frac {3}{2}}} \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 20
DSolve[4*x^2*y''[x]+8*x*y'[x]-3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 x^2+c_1}{x^{3/2}} \\ \end{align*}