60.2.191 problem 767

Internal problem ID [10778]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 767
Date solved : Monday, January 27, 2025 at 09:43:59 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {-8 y x -x^{3}+2 x^{2}-8 x +32}{32 y+4 x^{2}-8 x +32} \end{align*}

✓ Solution by Maple

Time used: 0.038 (sec). Leaf size: 26

dsolve(diff(y(x),x) = (-8*x*y(x)-x^3+2*x^2-8*x+32)/(32*y(x)+4*x^2-8*x+32),y(x), singsol=all)
 

\[ y = -\frac {x^{2}}{8}+4 \operatorname {LambertW}\left (\frac {c_{1} {\mathrm e}^{-\frac {x}{16}-\frac {3}{4}}}{4}\right )+\frac {x}{4}+3 \]

✓ Solution by Mathematica

Time used: 0.887 (sec). Leaf size: 53

DSolve[D[y[x],x] == (32 - 8*x + 2*x^2 - x^3 - 8*x*y[x])/(32 - 8*x + 4*x^2 + 32*y[x]),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to 4 W\left (-e^{-\frac {x}{16}-1+c_1}\right )-\frac {x^2}{8}+\frac {x}{4}+3 \\ y(x)\to -\frac {x^2}{8}+\frac {x}{4}+3 \\ \end{align*}