60.2.236 problem 812

Internal problem ID [10823]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 812
Date solved : Tuesday, January 28, 2025 at 05:18:06 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

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

✓ Solution by Maple

Time used: 0.279 (sec). Leaf size: 30

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

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

✓ Solution by Mathematica

Time used: 0.644 (sec). Leaf size: 76

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

\[ y(x)\to -\frac {3 x^8}{32}-\frac {x^7}{4}-\frac {x^6}{6}-\frac {3 x^5}{4}+\left (-1+\frac {3 c_1}{4}\right ) x^4+\left (\frac {1}{6}+c_1\right ) x^3-\frac {3 x^2}{2}+3 c_1 x-\frac {3 c_1{}^2}{2} \]