76.1.14 problem 14

Internal problem ID [17313]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.1 (Separable equations). Problems at page 44
Problem number : 14
Date solved : Tuesday, January 28, 2025 at 09:59:37 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {3-2 x}{y} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=-6 \end{align*}

✓ Solution by Maple

Time used: 0.199 (sec). Leaf size: 18

dsolve([diff(y(x),x)=(3-2*x)/y(x),y(1) = -6],y(x), singsol=all)
 

\[ y = -\sqrt {-2 x^{2}+6 x +32} \]

✓ Solution by Mathematica

Time used: 0.096 (sec). Leaf size: 21

DSolve[{D[y[x],x]==(3-2*x)/y[x],{y[1]==-6}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\sqrt {-2 x^2+6 x+32} \]