12.3.10 problem 11

Internal problem ID [1587]
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 : 11
Date solved : Saturday, March 29, 2025 at 11:00:45 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (1\right )&=4 \end{align*}

✓ Maple. Time used: 0.090 (sec). Leaf size: 25

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

\[ y = 2+\frac {\sqrt {6 x^{3}+27 x^{2}+36 x -33}}{3} \]

✓ Mathematica. Time used: 0.154 (sec). Leaf size: 30

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

\[ y(x)\to \sqrt {\frac {2 x^3}{3}+3 x^2+4 x-\frac {11}{3}}+2 \]

✓ Sympy. Time used: 0.398 (sec). Leaf size: 24

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

\[ y{\left (x \right )} = \frac {\sqrt {6 x^{3} + 27 x^{2} + 36 x - 33}}{3} + 2 \]