58.2.8 problem 9

Internal problem ID [9131]
Book : Second order enumerated odes
Section : section 2
Problem number : 9
Date solved : Tuesday, January 28, 2025 at 04:00:08 PM
CAS classification : [_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} y^{\prime \prime }+\left (x +3\right ) y^{\prime }+\left (3+y^{2}\right ) {y^{\prime }}^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 32

dsolve(diff(y(x),x$2)+(3+x)*diff(y(x),x)+(3+y(x)^2)*(diff(y(x),x))^2=0,y(x), singsol=all)
 

\[ c_{1} \operatorname {erf}\left (\frac {\sqrt {2}\, \left (x +3\right )}{2}\right )-c_{2} +\int _{}^{y}{\mathrm e}^{\frac {\textit {\_a} \left (\textit {\_a}^{2}+9\right )}{3}}d \textit {\_a} = 0 \]

✓ Solution by Mathematica

Time used: 9.111 (sec). Leaf size: 56

DSolve[D[y[x],{x,2}]+(3+x)*D[y[x],x]+(3+y[x]^2)*(D[y[x],x])^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}e^{\frac {K[2]^3}{3}+3 K[2]}dK[2]\&\right ]\left [\int _1^x-e^{-\frac {1}{2} K[3] (K[3]+6)} c_1dK[3]+c_2\right ] \]