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 : Monday, January 27, 2025 at 05:09:04 AM
CAS classification : [_separable]

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

✓ Solution by Maple

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

dsolve(diff(y(x),x)= (3*x^2+2*x+1)/(y(x)-2),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*}

✓ Solution by Mathematica

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

DSolve[D[y[x],x]== (3*x^2+2*x+1)/(y[x]-2),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*}