75.4.25 problem 90

Internal problem ID [16656]
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 : Monday, March 31, 2025 at 03:03:48 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 13

ode:=exp(diff(y(x),x)) = x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x \ln \left (x \right )-x +c_1 \]

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

ode=Exp[D[y[x],x]]==x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.155 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x + exp(Derivative(y(x), x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + x \log {\left (x \right )} - x \]