60.2.181 problem 757

Internal problem ID [10768]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 757
Date solved : Monday, January 27, 2025 at 09:43:11 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {-4 y x +x^{3}+2 x^{2}-4 x -8}{-8 y+2 x^{2}+4 x -8} \end{align*}

✓ Solution by Maple

Time used: 0.037 (sec). Leaf size: 26

dsolve(diff(y(x),x) = (-4*x*y(x)+x^3+2*x^2-4*x-8)/(-8*y(x)+2*x^2+4*x-8),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.893 (sec). Leaf size: 49

DSolve[D[y[x],x] == (-8 - 4*x + 2*x^2 + x^3 - 4*x*y[x])/(-8 + 4*x + 2*x^2 - 8*y[x]),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{4} \left (8 W\left (-e^{-\frac {x}{4}-1+c_1}\right )+x^2+2 x+4\right ) \\ y(x)\to \frac {1}{4} \left (x^2+2 x+4\right ) \\ \end{align*}