64.5.8 problem 8

Internal problem ID [13242]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number : 8
Date solved : Wednesday, March 05, 2025 at 09:31:09 PM
CAS classification : [_linear]

\begin{align*} \left (x^{2}+x -2\right ) y^{\prime }+3 \left (x +1\right ) y&=x -1 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 24

ode:=(x^2+x-2)*diff(y(x),x)+3*(1+x)*y(x) = x-1; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.087 (sec). Leaf size: 76

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

\[ y(x)\to \exp \left (\int _1^x-\frac {3 (K[1]+1)}{K[1]^2+K[1]-2}dK[1]\right ) \left (\int _1^x\frac {\exp \left (-\int _1^{K[2]}-\frac {3 (K[1]+1)}{K[1]^2+K[1]-2}dK[1]\right )}{K[2]+2}dK[2]+c_1\right ) \]

✓ Sympy. Time used: 0.398 (sec). Leaf size: 22

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

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