2.188 problem 764

Internal problem ID [8344]

Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 764.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x),G(x)*y+H(x)]]]

Solve \begin {gather*} \boxed {y^{\prime }-\frac {\left (-\ln \relax (y) x -\ln \relax (y)+x^{4}\right ) y}{x \left (x +1\right )}=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 36

dsolve(diff(y(x),x) = (-ln(y(x))*x-ln(y(x))+x^4)*y(x)/x/(x+1),y(x), singsol=all)
 

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

Solution by Mathematica

Time used: 0.395 (sec). Leaf size: 43

DSolve[y'[x] == ((x^4 - Log[y[x]] - x*Log[y[x]])*y[x])/(x*(1 + x)),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to (x+1)^{\frac {1}{x}} \exp \left (-\frac {x (x ((4-3 x) x-6)+12)+25+12 c_1}{12 x}\right ) \\ \end{align*}