60.2.60 problem 636

Internal problem ID [10647]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 636
Date solved : Monday, January 27, 2025 at 09:21:01 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} y^{\prime }&=\left (-\ln \left (y\right )+x^{2}\right ) y \end{align*}

Solution by Maple

Time used: 0.115 (sec). Leaf size: 19

dsolve(diff(y(x),x) = (-ln(y(x))+x^2)*y(x),y(x), singsol=all)
 
\[ y = {\mathrm e}^{c_{1} {\mathrm e}^{-x}+x^{2}-2 x +2} \]

Solution by Mathematica

Time used: 0.320 (sec). Leaf size: 24

DSolve[D[y[x],x] == (x^2 - Log[y[x]])*y[x],y[x],x,IncludeSingularSolutions -> True]
 
\[ y(x)\to e^{x^2-2 x-2 c_1 e^{-x}+2} \]