68.4.56 problem 56

Internal problem ID [17236]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 56
Date solved : Thursday, October 02, 2025 at 01:59:26 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.019 (sec). Leaf size: 13

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

\[ y = -\frac {1}{3}+\frac {4 \left (x +3\right )^{3}}{81} \]

✓ Mathematica. Time used: 0.041 (sec). Leaf size: 26

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

\begin{align*} y(x)&\to \frac {4 x^3}{81}+\frac {4 x^2}{9}+\frac {4 x}{3}+1 \end{align*}

✓ Sympy. Time used: 0.182 (sec). Leaf size: 22

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

\[ y{\left (x \right )} = \frac {4 x^{3}}{81} + \frac {4 x^{2}}{9} + \frac {4 x}{3} + 1 \]