Internal problem ID [9088]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 753.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [`x=_G(y,y')`]
\[ \boxed {y^{\prime }-\frac {\left (x +1+x^{4} \ln \left (y\right )\right ) y \ln \left (y\right )}{x \left (x +1\right )}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 38
dsolve(diff(y(x),x) = (x+1+x^4*ln(y(x)))*y(x)*ln(y(x))/x/(x+1),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-\frac {12 x}{3 x^{4}-4 x^{3}+6 x^{2}+12 \ln \left (x +1\right )-12 c_{1} -12 x}} \]
✓ Solution by Mathematica
Time used: 0.5 (sec). Leaf size: 46
DSolve[y'[x] == (Log[y[x]]*(1 + x + x^4*Log[y[x]])*y[x])/(x*(1 + x)),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \exp \left (\frac {12 x}{-3 x^4+4 x^3-6 x^2+12 x-12 \log (x+1)+12 c_1}\right ) \\ y(x)\to 1 \\ \end{align*}