68.4.53 problem 53

Internal problem ID [17233]
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 : 53
Date solved : Thursday, October 02, 2025 at 01:59:17 PM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.028 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 18

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

\begin{align*} y(x)&\to 4 \sqrt [3]{3 x+1}-3 \end{align*}

✓ Sympy. Time used: 0.143 (sec). Leaf size: 14

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

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