2.185 problem 761

Internal problem ID [8341]

Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 761.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational, [_Abel, 2nd type, class A]]

Solve \begin {gather*} \boxed {y^{\prime }-\frac {-4 y x -x^{3}+4 x^{2}-4 x +8}{8 y+2 x^{2}-8 x +8}=0} \end {gather*}

Solution by Maple

Time used: 0.063 (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)
 

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

Solution by Mathematica

Time used: 60.025 (sec). Leaf size: 26

DSolve[y'[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 \text {ProductLog}\left (-e^{-x-1+c_1}\right )-\frac {x^2}{4}+x \\ \end{align*}