76.1.14 problem 14

Internal problem ID [17242]
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 : Monday, March 31, 2025 at 03:45:55 PM
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*}

✓ Maple. Time used: 0.109 (sec). Leaf size: 18

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

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

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

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

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

✓ Sympy. Time used: 0.418 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-(3 - 2*x)/y(x) + Derivative(y(x), x),0) 
ics = {y(1): -6} 
dsolve(ode,func=y(x),ics=ics)
 

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