Internal problem ID [14881]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number: 60.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {5 x^{2} y^{\prime \prime }-y^{\prime } x +2 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(5*x^2*diff(y(x),x$2)-x*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = x^{\frac {3}{5}} \left (c_{1} \sin \left (\frac {\ln \left (x \right )}{5}\right )+c_{2} \cos \left (\frac {\ln \left (x \right )}{5}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 32
DSolve[5*x^2*y''[x]-x*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^{3/5} \left (c_2 \cos \left (\frac {\log (x)}{5}\right )+c_1 \sin \left (\frac {\log (x)}{5}\right )\right ) \]