Internal problem ID [5263]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 3. Linear equations with variable coefficients. Page 124
Problem number: 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-2 y=0} \end {gather*} Given that one solution of the ode is \begin {align*} y_1 &= x^{2} \end {align*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 15
dsolve([x^2*diff(y(x),x$2)-2*y(x)=0,x^2],y(x), singsol=all)
\[ y \relax (x ) = c_{1} x^{2}+\frac {c_{2}}{x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 18
DSolve[x^2*y''[x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 x^3+c_1}{x} \\ \end{align*}