60.2.292 problem 869

Internal problem ID [10879]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 869
Date solved : Tuesday, January 28, 2025 at 05:28:25 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {-x +1-2 y+3 x^{2}-2 x^{2} y+2 x^{4}+x^{3}-2 x^{3} y+2 x^{5}}{x^{2}-y} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 34

dsolve(diff(y(x),x) = 1/(x^2-y(x))*(-x+1-2*y(x)+3*x^2-2*x^2*y(x)+2*x^4+x^3-2*x^3*y(x)+2*x^5),y(x), singsol=all)
 

\[ y = x^{2}+\frac {\operatorname {LambertW}\left (-2 c_{1} {\mathrm e}^{x^{4}+\frac {4}{3} x^{3}-2 x^{2}+4 x -1}\right )}{2}+\frac {1}{2} \]

✓ Solution by Mathematica

Time used: 1.018 (sec). Leaf size: 53

DSolve[D[y[x],x] == (1 - x + 3*x^2 + x^3 + 2*x^4 + 2*x^5 - 2*y[x] - 2*x^2*y[x] - 2*x^3*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+\frac {4 x^3}{3}-2 x^2+4 x-1+c_1}\right )\right ) \\ y(x)\to x^2+\frac {1}{2} \\ \end{align*}