Internal problem ID [9099]
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)]`]]
\[ \boxed {y^{\prime }-\frac {\left (-\ln \left (y\right ) x -\ln \left (y\right )+x^{4}\right ) y}{x \left (x +1\right )}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 40
dsolve(diff(y(x),x) = (-ln(y(x))*x-ln(y(x))+x^4)*y(x)/x/(x+1),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{\frac {3 x^{4}-4 x^{3}+6 x^{2}+12 c_{1} -12 x}{12 x}} \left (x +1\right )^{\frac {1}{x}} \]
✓ Solution by Mathematica
Time used: 0.391 (sec). Leaf size: 46
DSolve[y'[x] == ((x^4 - Log[y[x]] - x*Log[y[x]])*y[x])/(x*(1 + x)),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to (x+1)^{\frac {1}{x}} \exp \left (-\frac {-3 x^4+4 x^3-6 x^2+12 x+25+12 c_1}{12 x}\right ) \]