Internal problem ID [9040]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 705.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]
\[ \boxed {y^{\prime }-\frac {\left (\ln \left (y\right )+x +x^{3}+x^{4}\right ) y}{x}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(x),x) = (ln(y(x))+x+x^3+x^4)*y(x)/x,y(x), singsol=all)
\[ y \left (x \right ) = x^{x} {\mathrm e}^{c_{1} x +\frac {1}{2} x^{3}+\frac {1}{3} x^{4}} \]
✓ Solution by Mathematica
Time used: 0.346 (sec). Leaf size: 30
DSolve[y'[x] == ((x + x^3 + x^4 + Log[y[x]])*y[x])/x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^x e^{\frac {x^4}{3}+\frac {x^3}{2}+c_1 x} \]