60.2.129 problem 705

Internal problem ID [10716]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 705
Date solved : Monday, January 27, 2025 at 09:29:37 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} y^{\prime }&=\frac {\left (\ln \left (y\right )+x +x^{3}+x^{4}\right ) y}{x} \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 23

dsolve(diff(y(x),x) = (ln(y(x))+x+x^3+x^4)*y(x)/x,y(x), singsol=all)
 

\[ y = x^{x} {\mathrm e}^{\frac {1}{2} x^{3}+c_{1} x +\frac {1}{3} x^{4}} \]

✓ Solution by Mathematica

Time used: 0.400 (sec). Leaf size: 32

DSolve[D[y[x],x] == ((x + x^3 + x^4 + Log[y[x]])*y[x])/x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^x e^{\frac {1}{6} x \left (2 x^3+3 x^2+3+6 c_1\right )} \]