2.78 problem 654

Internal problem ID [8234]

Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 654.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x),G(x)]]]

Solve \begin {gather*} \boxed {y^{\prime }+\frac {2 x^{2}+2 x -3 \sqrt {x^{2}+3 y}}{3 x +3}=0} \end {gather*}

Solution by Maple

Time used: 0.343 (sec). Leaf size: 23

dsolve(diff(y(x),x) = -1/3*(2*x^2+2*x-3*(x^2+3*y(x))^(1/2))/(x+1),y(x), singsol=all)
 

\[ c_{1}+\frac {3 \ln \left (x +1\right )}{2}-\sqrt {x^{2}+3 y \relax (x )} = 0 \]

Solution by Mathematica

Time used: 0.43 (sec). Leaf size: 36

DSolve[y'[x] == ((-2*x)/3 - (2*x^2)/3 + Sqrt[x^2 + 3*y[x]])/(1 + x),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{12} \left (-4 x^2+9 \log (x+1) (\log (x+1)-2 c_1)+9 c_1{}^2\right ) \\ \end{align*}