60.2.90 problem 666

Internal problem ID [10677]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 666
Date solved : Monday, January 27, 2025 at 09:25:03 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} y^{\prime }&=\left (-\ln \left (y\right )+1+x^{2}+x^{3}\right ) y \end{align*}

✓ Solution by Maple

Time used: 0.135 (sec). Leaf size: 24

dsolve(diff(y(x),x) = (-ln(y(x))+1+x^2+x^3)*y(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.398 (sec). Leaf size: 29

DSolve[D[y[x],x] == (1 + x^2 + x^3 - Log[y[x]])*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{x^3-2 x^2+4 x-c_1 e^{-x}-3} \]