60.2.49 problem 625

Internal problem ID [10636]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 625
Date solved : Tuesday, January 28, 2025 at 05:00:26 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(y)]`]]

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

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 53

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

\[ i \ln \left (x^{3}-6 y-1\right )+2 \sqrt {-x^{3}+6 y}-2 \arctan \left (\sqrt {-x^{3}+6 y}\right )+2 i x^{3}-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 5.228 (sec). Leaf size: 69

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

\begin{align*} y(x)\to \frac {1}{6} \left (-W\left (-i e^{-x^3-1-6 c_1}\right ){}^2-2 W\left (-i e^{-x^3-1-6 c_1}\right )+x^3-1\right ) \\ y(x)\to \frac {1}{6} \left (x^3-1\right ) \\ \end{align*}