Internal problem ID [6693]
Book: Second order enumerated odes
Section: section 2
Problem number: 9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\left (3+x \right ) y^{\prime }+\left (3+y^{2}\right ) \left (y^{\prime }\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.049 (sec). Leaf size: 37
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)
\[ c_{1} \erf \left (\frac {x \sqrt {2}}{2}+\frac {3 \sqrt {2}}{2}\right )-c_{2}+\int _{}^{y \relax (x )}{\mathrm e}^{\frac {1}{3} \textit {\_a}^{3}+3 \textit {\_a}}d \textit {\_a} = 0 \]
✓ Solution by Mathematica
Time used: 0.189 (sec). Leaf size: 61
DSolve[y''[x]+(3+x)*y'[x]+(3+y[x]^2)*(y'[x])^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} 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 ] \\ \end{align*}