Internal problem ID [937]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x^{2}+3 x +2}{y-2}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.045 (sec). Leaf size: 25
dsolve([diff(y(x),x)=(x^2+3*x+2)/(y(x)-2),y(1) = 4],y(x), singsol=all)
\[ y \relax (x ) = 2+\frac {\sqrt {6 x^{3}+27 x^{2}+36 x -33}}{3} \]
✓ Solution by Mathematica
Time used: 0.128 (sec). Leaf size: 30
DSolve[{y'[x]==(x^2+3*x+2)/(y[x]-2),y[1]==4},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {\frac {2 x^3}{3}+3 x^2+4 x-\frac {11}{3}}+2 \\ \end{align*}