Internal problem ID [4849]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 7. Other second-Order equations.
page 435
Problem number: 16 (b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {x^{2} y^{\prime \prime }+x y^{\prime }-4 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)-4*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{2} x^{4}+c_{1}}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 18
DSolve[x^2*y''[x]+x*y'[x]-4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_2 x^4+c_1}{x^2} \]