69.2.9 problem 29

Internal problem ID [17973]
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 : 29
Date solved : Thursday, October 02, 2025 at 02:31:46 PM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 16

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

\[ y = x^{2}+2 x +2+{\mathrm e}^{x} c_1 \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 31

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

\begin{align*} y(x)&\to e^x \left (\int _1^x-e^{-K[1]} K[1]^2dK[1]+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.066 (sec). Leaf size: 15

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

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