44.3.10 problem 18

Internal problem ID [6991]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Review problems at page 34
Problem number : 18
Date solved : Monday, January 27, 2025 at 02:40:03 PM
CAS classification : [_separable]

\begin{align*} \left (2 y-2\right ) y^{\prime }&=2 x -1 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.049 (sec). Leaf size: 27

dsolve([(2*y(x)-2)*diff(y(x),x)=2*x-1,y(0) = 1],y(x), singsol=all)
 

\begin{align*} y &= 1-\sqrt {\left (x -1\right ) x} \\ y &= 1+\sqrt {\left (x -1\right ) x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.090 (sec). Leaf size: 33

DSolve[{(2*y[x]-2)*D[y[x],x]==2*x-1,{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to 1-\sqrt {(x-1) x} \\ y(x)\to \sqrt {(x-1) x}+1 \\ \end{align*}