44.5.35 problem 35

Internal problem ID [7097]
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 : 35
Date solved : Sunday, March 30, 2025 at 11:42:02 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {3 x +1}{2 y} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.105 (sec). Leaf size: 18

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

\[ y = -\frac {\sqrt {6 x^{2}+4 x -12}}{2} \]

✓ Mathematica. Time used: 0.088 (sec). Leaf size: 21

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

\[ y(x)\to -\sqrt {\frac {3 x^2}{2}+x-3} \]

✓ Sympy. Time used: 0.552 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = - \frac {\sqrt {6 x^{2} + 4 x - 12}}{2} \]