12.3.22 problem 23

Internal problem ID [1599]
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 : 23
Date solved : Tuesday, March 04, 2025 at 12:53:43 PM
CAS classification : [_separable]

\begin{align*} \left (x +1\right ) \left (x -2\right ) y^{\prime }+y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=-3 \end{align*}

✓ Maple. Time used: 0.028 (sec). Leaf size: 26

ode:=(1+x)*(x-2)*diff(y(x),x)+y(x) = 0; 
ic:=y(1) = -3; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -\frac {3 \left (1+i \sqrt {3}\right ) 2^{{2}/{3}} \left (x +1\right )^{{1}/{3}}}{4 \left (x -2\right )^{{1}/{3}}} \]

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 23

ode=(x+1)*(x-2)*D[y[x],x]+y[x]==0; 
ic=y[1]==-3; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\frac {3 \sqrt [3]{x+1}}{\sqrt [3]{4-2 x}} \]

✓ Sympy. Time used: 0.353 (sec). Leaf size: 100

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

\[ y{\left (x \right )} = \frac {\sqrt [3]{x + 1} \left (\frac {3 \sqrt [3]{2}}{2} + \frac {3 \cdot 2^{\frac {2}{3}}}{2} + 3 - 3 \sqrt [3]{-1} \cdot 2^{\frac {2}{3}} - 3 \sqrt [3]{-1} - \frac {3 \sqrt [3]{-2}}{2} + \frac {3 \left (-1\right )^{\frac {2}{3}} \sqrt [3]{2}}{2} + \frac {3 \left (-2\right )^{\frac {2}{3}}}{2} + 3 \left (-1\right )^{\frac {2}{3}}\right )}{\sqrt [3]{x - 2}} \]