Internal problem ID [6721]
Book: Second order enumerated odes
Section: section 2
Problem number: 36.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+\left (x y^{\prime }-y\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.141 (sec). Leaf size: 22
dsolve(x^2*diff(y(x),x$2)+(x*diff(y(x),x)-y(x))^2=0,y(x), singsol=all)
\[ y \relax (x ) = \left (-{\mathrm e}^{c_{1}} \expIntegral \left (1, -\ln \left (\frac {1}{x}\right )+c_{1}\right )+c_{2}\right ) x \]
✓ Solution by Mathematica
Time used: 0.535 (sec). Leaf size: 25
DSolve[x^2*y''[x]+(x*y'[x]-y[x])^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \left (e^{c_1} \text {Ei}(-c_1-\log (x))+c_2\right ) \\ \end{align*}