44.5.55 problem 48 (b 1)

Internal problem ID [7117]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 48 (b 1)
Date solved : Tuesday, February 04, 2025 at 12:15:40 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 13

dsolve([diff(y(x),x)=1/(y(x)-3),y(0) = 4],y(x), singsol=all)
 

\[ y = 3+\sqrt {1+2 x} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 16

DSolve[{D[y[x],x]==1/(y[x]-3),{y[0]==4}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sqrt {2 x+1}+3 \]