65.5.1 problem 1

Internal problem ID [15684]
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 : Thursday, October 02, 2025 at 10:23:09 AM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Maple. Time used: 0.021 (sec). Leaf size: 12

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

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 17

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

\begin{align*} y(x)&\to \frac {3 x^2}{2}+x-\frac {1}{2} \end{align*}

✓ Sympy. Time used: 0.067 (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)
 

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