2.1.1 problem 1

Internal problem ID [651]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.2. Integrals as general and particular solutions. Page 16
Problem number : 1
Date solved : Tuesday, September 30, 2025 at 04:04:59 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=1+2 x \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=3 \\ \end{align*}

✓ Maple. Time used: 0.023 (sec). Leaf size: 10

ode:=diff(y(x),x) = 1+2*x; 
ic:=[y(0) = 3]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = x^{2}+x +3 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 11

ode=D[y[x],x]==1+2*x; 
ic=y[0]==3; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x^2+x+3 \end{align*}

✓ Sympy. Time used: 0.082 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x + Derivative(y(x), x) - 1,0) 
ics = {y(0): 3} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x^{2} + x + 3 \]