Internal problem ID [928]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {3 x^{2}+2 x +1}{y-2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (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 \relax (x ) = 2-\sqrt {2 x^{3}+2 x^{2}+2 x +2 c_{1}+4} \\ y \relax (x ) = 2+\sqrt {2 x^{3}+2 x^{2}+2 x +2 c_{1}+4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.152 (sec). Leaf size: 56
DSolve[y'[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*}