77.1.43 problem 60 (page 103)

Internal problem ID [17854]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 60 (page 103)
Date solved : Thursday, March 13, 2025 at 11:01:06 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=2 x y-x^{3}+x \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

ode:=diff(y(x),x) = 2*x*y(x)-x^3+x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x^{2}}{2}+{\mathrm e}^{x^{2}} c_{1} \]

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 21

ode=D[y[x],x]==2*x*y[x]-x^3+x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.257 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3 - 2*x*y(x) - x + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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