58.2.36 problem 36

Internal problem ID [9159]
Book : Second order enumerated odes
Section : section 2
Problem number : 36
Date solved : Tuesday, January 28, 2025 at 04:00:12 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+\left (-y+x y^{\prime }\right )^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.036 (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)
 

\[ y = \left (-{\mathrm e}^{c_{1}} \operatorname {Ei}_{1}\left (-\ln \left (\frac {1}{x}\right )+c_{1} \right )+c_{2} \right ) x \]

✓ Solution by Mathematica

Time used: 28.572 (sec). Leaf size: 33

DSolve[x^2*D[y[x],{x,2}]+(x*D[y[x],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*}