60.2.304 problem 881

Internal problem ID [10891]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 881
Date solved : Monday, January 27, 2025 at 10:21:30 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, [_Abel, `2nd type`, `class C`]]

\begin{align*} y^{\prime }&=\frac {-18 y x -6 x^{3}-18 x +27 y^{3}+27 x^{2} y^{2}+9 y x^{4}+x^{6}}{27 y+9 x^{2}+27} \end{align*}

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 77

dsolve(diff(y(x),x) = (-18*x*y(x)-6*x^3-18*x+27*y(x)^3+27*x^2*y(x)^2+9*y(x)*x^4+x^6)/(27*y(x)+9*x^2+27),y(x), singsol=all)
 

\begin{align*} y &= \frac {-2 c_{1} x^{2}+2 x^{3}+3 \sqrt {-2 x +2 c_{1} +1}+3}{-6 x +6 c_{1}} \\ y &= \frac {-2 c_{1} x^{2}+2 x^{3}-3 \sqrt {-2 x +2 c_{1} +1}+3}{-6 x +6 c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.374 (sec). Leaf size: 68

DSolve[D[y[x],x] == (-18*x - 6*x^3 + x^6 - 18*x*y[x] + 9*x^4*y[x] + 27*x^2*y[x]^2 + 27*y[x]^3)/(27 + 9*x^2 + 27*y[x]),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {x^2}{3}+\frac {27}{-27+\sqrt {-1458 x+c_1}} \\ y(x)\to -\frac {x^2}{3}-\frac {27}{27+\sqrt {-1458 x+c_1}} \\ y(x)\to -\frac {x^2}{3} \\ \end{align*}