75.6.13 problem 137

Internal problem ID [16698]
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 : 137
Date solved : Monday, March 31, 2025 at 03:06:12 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }-y \,{\mathrm e}^{x}&=2 x \,{\mathrm e}^{{\mathrm e}^{x}} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

ode:=diff(y(x),x)-y(x)*exp(x) = 2*x*exp(exp(x)); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (x^{2}+c_1 \right ) {\mathrm e}^{{\mathrm e}^{x}} \]

✓ Mathematica. Time used: 0.056 (sec). Leaf size: 17

ode=D[y[x],x]-y[x]*Exp[x]==2*x*Exp[ Exp[x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{e^x} \left (x^2+c_1\right ) \]

✓ Sympy. Time used: 0.275 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x*exp(exp(x)) - y(x)*exp(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + x^{2}\right ) e^{e^{x}} \]