75.6.14 problem 138

Internal problem ID [16699]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page 54
Problem number : 138
Date solved : Monday, March 31, 2025 at 03:06:14 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }+x y \,{\mathrm e}^{x}&={\mathrm e}^{\left (1-x \right ) {\mathrm e}^{x}} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

ode:=diff(y(x),x)+x*y(x)*exp(x) = exp((1-x)*exp(x)); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (x +c_1 \right ) {\mathrm e}^{-\left (-1+x \right ) {\mathrm e}^{x}} \]

✓ Mathematica. Time used: 0.091 (sec). Leaf size: 20

ode=D[y[x],x]+x*y[x]*Exp[x]==Exp[ (1-x)*Exp[x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-e^x (x-1)} (x+c_1) \]

✓ Sympy. Time used: 0.461 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*y(x)*exp(x) - exp((1 - x)*exp(x)) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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