2.36 problem 36

Internal problem ID [8125]
Book : Second order enumerated odes
Section : section 2
Problem number : 36
Date solved : Tuesday, October 22, 2024 at 03:00:25 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

Solve

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

2.36.1 Maple step by step solution

2.36.2 Maple trace

Methods for second order ODEs:
 

2.36.3 Maple dsolve solution

Solving time : 0.021 (sec)
Leaf size : 22

dsolve(x^2*diff(diff(y(x),x),x)+(x*diff(y(x),x)-y(x))^2 = 0, 
       y(x),singsol=all)
 

\[ y = \left (-{\mathrm e}^{c_1} \operatorname {Ei}_{1}\left (-\ln \left (\frac {1}{x}\right )+c_1 \right )+c_2 \right ) x \]

2.36.4 Mathematica DSolve solution

Solving time : 43.474 (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*}