60.2.55 problem 631

Internal problem ID [10642]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 631
Date solved : Monday, January 27, 2025 at 09:20:08 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(y)]`]]

\begin{align*} y^{\prime }&=\frac {x^{2} \left (1+2 \sqrt {x^{3}-6 y}\right )}{2} \end{align*}

✓ Solution by Maple

Time used: 0.169 (sec). Leaf size: 23

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

\[ c_{1} -x^{3}-\frac {1}{4}-\sqrt {x^{3}-6 y} = 0 \]

✓ Solution by Mathematica

Time used: 0.335 (sec). Leaf size: 31

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

\[ y(x)\to \frac {1}{6} \left (-x^6+(1-12 c_1) x^3-36 c_1{}^2\right ) \]