Internal problem ID [13218]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 14. Higher order equations and the reduction of order method. Additional
exercises page 277
Problem number: 14.2 (c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {x^{2} y^{\prime \prime }-6 x y^{\prime }+12 y=0} \] Given that one solution of the ode is \begin {align*} y_1 &= x^{3} \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve([x^2*diff(y(x),x$2)-6*x*diff(y(x),x)+12*y(x)=0,x^3],y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x^{4}+c_{2} x^{3} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 16
DSolve[x^2*y''[x]-6*x*y'[x]+12*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^3 (c_2 x+c_1) \]