75.2.10 problem 30

Internal problem ID [16608]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 2. The method of isoclines. Exercises page 27
Problem number : 30
Date solved : Thursday, March 13, 2025 at 08:25:54 AM
CAS classification : [[_linear, `class A`]]

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

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

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

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

✓ Mathematica. Time used: 0.07 (sec). Leaf size: 17

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

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

✓ Sympy. Time used: 0.116 (sec). Leaf size: 10

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

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