60.2.80 problem 656

Internal problem ID [10667]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 656
Date solved : Monday, January 27, 2025 at 09:23:20 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^{3}\right ) y}{x} \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 15

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

\[ y = {\mathrm e}^{\frac {x \left (x^{2}+2 c_{1} \right )}{2}} \]

✓ Solution by Mathematica

Time used: 0.279 (sec). Leaf size: 20

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

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