60.2.68 problem 644

Internal problem ID [10655]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 644
Date solved : Tuesday, January 28, 2025 at 05:02:37 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

\begin{align*} y^{\prime }&=-\frac {x^{2} \left (a x -2 \sqrt {a \left (a \,x^{4}+8 y\right )}\right )}{2} \end{align*}

✓ Solution by Maple

Time used: 0.105 (sec). Leaf size: 27

dsolve(diff(y(x),x) = -1/2*x^2*(a*x-2*(a*(a*x^4+8*y(x)))^(1/2)),y(x), singsol=all)
 

\[ c_{1} +\frac {4 a \,x^{3}}{3}-\sqrt {a \left (a \,x^{4}+8 y\right )} = 0 \]

✓ Solution by Mathematica

Time used: 0.556 (sec). Leaf size: 34

DSolve[D[y[x],x] == -1/2*(x^2*(a*x - 2*Sqrt[a*(a*x^4 + 8*y[x])])),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{72} a \left (16 x^6-9 x^4-96 c_1 x^3+144 c_1{}^2\right ) \]