60.2.185 problem 761

Internal problem ID [10772]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 761
Date solved : Monday, January 27, 2025 at 09:43:25 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 0.835 (sec). Leaf size: 38

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

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