Internal problem ID [7477]
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]]
\[ \boxed {x^{2} y^{\prime \prime }+\left (x y^{\prime }-y\right )^{2}=0} \]
✓ Solution by Maple
Time used: 0.032 (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)
\[ y \left (x \right ) = \left (-{\mathrm e}^{c_{1}} \operatorname {expIntegral}_{1}\left (-\ln \left (\frac {1}{x}\right )+c_{1} \right )+c_{2} \right ) x \]
✓ Solution by Mathematica
Time used: 46.789 (sec). Leaf size: 33
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} \operatorname {ExpIntegralEi}(-c_1-\log (x))+c_2\right ) \\ y(x)\to c_2 x \\ \end{align*}