58.2.9 problem 10

Internal problem ID [9132]
Book : Second order enumerated odes
Section : section 2
Problem number : 10
Date solved : Monday, January 27, 2025 at 05:48:36 PM
CAS classification : [_Liouville, [_2nd_order, _reducible, _mu_xy]]

\begin{align*} y^{\prime \prime }+x y^{\prime }+y {y^{\prime }}^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 37

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

\[ y = -i \operatorname {RootOf}\left (i \sqrt {\pi }\, \operatorname {erf}\left (\frac {\sqrt {2}\, x}{2}\right ) c_{1} +i \sqrt {2}\, c_{2} -\operatorname {erf}\left (\textit {\_Z} \right ) \sqrt {\pi }\right ) \sqrt {2} \]

✓ Solution by Mathematica

Time used: 1.341 (sec). Leaf size: 44

DSolve[D[y[x],{x,2}]+x*D[y[x],x]+y[x]*(D[y[x],x])^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -i \sqrt {2} \text {erf}^{-1}\left (i \left (\sqrt {\frac {2}{\pi }} c_2-c_1 \text {erf}\left (\frac {x}{\sqrt {2}}\right )\right )\right ) \]