75.4.25 problem 90

Internal problem ID [16727]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 4. Equations with variables separable and equations reducible to them. Exercises page 38
Problem number : 90
Date solved : Tuesday, January 28, 2025 at 09:19:41 AM
CAS classification : [_quadrature]

\begin{align*} {\mathrm e}^{y^{\prime }}&=x \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 13

dsolve(exp(diff(y(x),x))=x,y(x), singsol=all)
 

\[ y = c_{1} +\ln \left (x \right ) x -x \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 15

DSolve[Exp[D[y[x],x]]==x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -x+x \log (x)+c_1 \]