Internal problem ID [11723]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.1. Basic theory of linear differential equations. Exercises page
124
Problem number: 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y=0} \] Given that one solution of the ode is \begin {align*} y_1 &= x \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
dsolve([x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+4*y(x)=0,x],singsol=all)
\[ y \left (x \right ) = x \left (c_{1} x^{3}+c_{2} \right ) \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 16
DSolve[x^2*y''[x]-4*x*y'[x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x \left (c_2 x^3+c_1\right ) \]