Internal problem ID [5256]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 3. Linear equations with variable coefficients. Page 121
Problem number: 1(a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y=0} \end {gather*} Given that one solution of the ode is \begin {align*} y_1 &= x^{3} \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve([x^2*diff(y(x),x$2)-7*x*diff(y(x),x)+15*y(x)=0,x^3],y(x), singsol=all)
\[ y \relax (x ) = x^{5} c_{1}+x^{3} c_{2} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 18
DSolve[x^2*y''[x]-7*x*y'[x]+15*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^3 \left (c_2 x^2+c_1\right ) \\ \end{align*}