74.4.56 problem 56

Internal problem ID [15949]
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 : Tuesday, January 28, 2025 at 08:24:22 AM
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*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 13

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

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

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 26

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

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