71.5.1 problem 1

Internal problem ID [14318]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.3.1, page 57
Problem number : 1
Date solved : Wednesday, March 05, 2025 at 10:45:40 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=3 x +1 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=2 \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 12

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

\[ y = \frac {3}{2} x^{2}+x -\frac {1}{2} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 17

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

\[ y(x)\to \frac {3 x^2}{2}+x-\frac {1}{2} \]

✓ Sympy. Time used: 0.118 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = \frac {3 x^{2}}{2} + x - \frac {1}{2} \]