60.2.52 problem 628

Internal problem ID [10639]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 628
Date solved : Monday, January 27, 2025 at 09:19:57 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(y)]`]]

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

✓ Solution by Maple

Time used: 4.262 (sec). Leaf size: 23

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

\[ c_{1} +\frac {x^{2}}{3}+\frac {4}{27}-\frac {4 \sqrt {x^{2}+3 y}}{9} = 0 \]

✓ Solution by Mathematica

Time used: 0.289 (sec). Leaf size: 32

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

\[ y(x)\to \frac {1}{48} \left (9 x^4-2 (8+27 c_1) x^2+81 c_1{}^2\right ) \]