60.2.395 problem 972

Internal problem ID [10982]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 972
Date solved : Tuesday, January 28, 2025 at 05:40:18 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {x \left (-x^{2}+2 x^{2} y-2 x^{4}+1\right )}{y-x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 26

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

\[ y = x^{2}+\frac {\operatorname {LambertW}\left (-2 c_{1} {\mathrm e}^{x^{4}-2 x^{2}-1}\right )}{2}+\frac {1}{2} \]

✓ Solution by Mathematica

Time used: 0.829 (sec). Leaf size: 43

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

\begin{align*} y(x)\to x^2+\frac {1}{2} \left (1+W\left (-e^{x^4-2 x^2-1+c_1}\right )\right ) \\ y(x)\to x^2+\frac {1}{2} \\ \end{align*}