2.8 problem 9

Internal problem ID [8097]
Book : Second order enumerated odes
Section : section 2
Problem number : 9
Date solved : Tuesday, October 22, 2024 at 03:00:20 PM
CAS classification : [_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solve

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

2.8.1 Maple step by step solution

2.8.2 Maple trace

Methods for second order ODEs:
 

2.8.3 Maple dsolve solution

Solving time : 0.010 (sec)
Leaf size : 32

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

\[ c_1 \,\operatorname {erf}\left (\frac {\sqrt {2}\, \left (3+x \right )}{2}\right )-c_2 +\int _{}^{y}{\mathrm e}^{\frac {\textit {\_a} \left (\textit {\_a}^{2}+9\right )}{3}}d \textit {\_a} = 0 \]

2.8.4 Mathematica DSolve solution

Solving time : 0.609 (sec)
Leaf size : 61

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]
 

\[ y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}e^{\frac {K[1]^3}{3}+3 K[1]}dK[1]\&\right ]\left [c_2-e^{9/2} \sqrt {\frac {\pi }{2}} c_1 \text {erf}\left (\frac {x+3}{\sqrt {2}}\right )\right ] \]