12.3.1 problem 1

Internal problem ID [1578]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. separable equations. Section 2.2 Page 52
Problem number : 1
Date solved : Tuesday, March 04, 2025 at 12:40:28 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 53

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

\begin{align*} y &= 2-\sqrt {2 x^{3}+2 x^{2}+2 c_1 +2 x +4} \\ y &= 2+\sqrt {2 x^{3}+2 x^{2}+2 c_1 +2 x +4} \\ \end{align*}

✓ Mathematica. Time used: 0.122 (sec). Leaf size: 56

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

\begin{align*} y(x)\to 2-\sqrt {2} \sqrt {x^3+x^2+x+2+c_1} \\ y(x)\to 2+\sqrt {2} \sqrt {x^3+x^2+x+2+c_1} \\ \end{align*}

✓ Sympy. Time used: 0.313 (sec). Leaf size: 44

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

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