60.2.372 problem 949

Internal problem ID [10959]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 949
Date solved : Monday, January 27, 2025 at 10:32:04 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class C`]]

\begin{align*} y^{\prime }&=\frac {x^{2} y+x^{4}+2 x^{3}-3 x^{2}+y x +x +y^{3}+3 x^{2} y^{2}-3 x y^{2}+3 y x^{4}-6 x^{3} y+x^{6}-3 x^{5}}{x \left (y+x^{2}-x +1\right )} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 81

dsolve(diff(y(x),x) = (x^2*y(x)+x^4+2*x^3-3*x^2+x*y(x)+x+y(x)^3+3*x^2*y(x)^2-3*x*y(x)^2+3*y(x)*x^4-6*x^3*y(x)+x^6-3*x^5)/x/(y(x)+x^2-x+1),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.483 (sec). Leaf size: 65

DSolve[D[y[x],x] == (x - 3*x^2 + 2*x^3 + x^4 - 3*x^5 + x^6 + x*y[x] + x^2*y[x] - 6*x^3*y[x] + 3*x^4*y[x] - 3*x*y[x]^2 + 3*x^2*y[x]^2 + y[x]^3)/(x*(1 - x + x^2 + y[x])),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -x^2+x+\frac {1}{-1+\sqrt {-2 \log (x)+c_1}} \\ y(x)\to -x^2+x-\frac {1}{1+\sqrt {-2 \log (x)+c_1}} \\ y(x)\to -((x-1) x) \\ \end{align*}