69.6.3 problem 127

Internal problem ID [18046]
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 : 127
Date solved : Thursday, October 02, 2025 at 02:35:55 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

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

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

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 17

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

\begin{align*} y(x)&\to e^{x^2} \left (x^2+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.154 (sec). Leaf size: 12

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

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