60.2.75 problem 651

Internal problem ID [10662]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 651
Date solved : Monday, January 27, 2025 at 09:22:30 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^{2}\right ) y}{x} \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 10

dsolve(diff(y(x),x) = (ln(y(x))+x^2)*y(x)/x,y(x), singsol=all)
 

\[ y = {\mathrm e}^{\left (x +c_{1} \right ) x} \]

✓ Solution by Mathematica

Time used: 0.263 (sec). Leaf size: 15

DSolve[D[y[x],x] == ((x^2 + Log[y[x]])*y[x])/x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{x (x+2 c_1)} \]