60.2.70 problem 646

Internal problem ID [10657]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 646
Date solved : Monday, January 27, 2025 at 09:22:08 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

\begin{align*} y^{\prime }&=\frac {x^{3}+x^{2}+2 \sqrt {x^{3}-6 y}}{2+2 x} \end{align*}

✓ Solution by Maple

Time used: 0.254 (sec). Leaf size: 23

dsolve(diff(y(x),x) = 1/2*(x^3+x^2+2*(x^3-6*y(x))^(1/2))/(x+1),y(x), singsol=all)
 

\[ c_{1} -3 \ln \left (x +1\right )-\sqrt {x^{3}-6 y} = 0 \]

✓ Solution by Mathematica

Time used: 0.482 (sec). Leaf size: 35

DSolve[D[y[x],x] == (x^2/2 + x^3/2 + Sqrt[x^3 - 6*y[x]])/(1 + x),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{6} \left (x^3-9 \log ^2(x+1)+18 c_1 \log (x+1)-9 c_1{}^2\right ) \]