Internal problem ID [7449]
Internal file name [OUTPUT/6416_Sunday_June_05_2022_04_51_28_PM_59827055/index.tex]
Book: Second order enumerated odes
Section: section 2
Problem number: 9.
ODE order: 2.
ODE degree: 1.
The type(s) of ODE detected by this program : "unknown"
Maple gives the following as the ode type
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Unable to solve or complete the solution.
\[ \boxed {y^{\prime \prime }+\left (3+x \right ) y^{\prime }+\left (3+y^{2}\right ) {y^{\prime }}^{2}=0} \]
Maple trace
`Methods for second order ODEs: --- Trying classification methods --- trying 2nd order Liouville <- 2nd_order Liouville successful`
✓ Solution by Maple
Time used: 0.016 (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)
\[ c_{1} \operatorname {erf}\left (\frac {\sqrt {2}\, \left (x +3\right )}{2}\right )-c_{2} +\int _{}^{y \left (x \right )}{\mathrm e}^{\frac {\textit {\_a} \left (\textit {\_a}^{2}+9\right )}{3}}d \textit {\_a} = 0 \]
✓ Solution by Mathematica
Time used: 0.359 (sec). Leaf size: 61
DSolve[y''[x]+(3+x)*y'[x]+(3+y[x]^2)*(y'[x])^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}e^{\frac {K[1]^3}{3}+3 K[1]}dK[1]\&\right ]\left [c_2-e^{9/2} \sqrt {\frac {\pi }{2}} c_1 \text {erf}\left (\frac {x+3}{\sqrt {2}}\right )\right ] \]