74.4.53 problem 53

Internal problem ID [15946]
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 : Tuesday, January 28, 2025 at 08:24:11 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 15

dsolve([diff(y(x),x)=(y(x)+3)/(3*x+1),y(0) = 1],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 18

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

\[ y(x)\to 4 \sqrt [3]{3 x+1}-3 \]