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 : Monday, January 27, 2025 at 05:09:32 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.043 (sec). Leaf size: 25

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

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

✓ Solution by Mathematica

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

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

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