38.5.36 problem 36

Internal problem ID [8384]
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 : 36
Date solved : Tuesday, September 30, 2025 at 05:34:10 PM
CAS classification : [_separable]

\begin{align*} \left (2 y-2\right ) y^{\prime }&=3 x^{2}+4 x +2 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.088 (sec). Leaf size: 19

ode:=(2*y(x)-2)*diff(y(x),x) = 3*x^2+4*x+2; 
ic:=[y(1) = -2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 1-\sqrt {\left (x +2\right ) \left (x^{2}+2\right )} \]

✓ Mathematica. Time used: 0.095 (sec). Leaf size: 26

ode=(2*y[x]-2)*D[y[x],x]==3*x^2+4*x+2; 
ic={y[1]==-2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 1-\sqrt {x^3+2 x^2+2 x+4} \end{align*}

✓ Sympy. Time used: 0.305 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*x**2 - 4*x + (2*y(x) - 2)*Derivative(y(x), x) - 2,0) 
ics = {y(1): -2} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 1 - \sqrt {x^{3} + 2 x^{2} + 2 x + 4} \]