38.1.1 problem 1

Internal problem ID [6418]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 24. First order differential equations. Test excercise 24. page 1067
Problem number : 1
Date solved : Sunday, March 30, 2025 at 10:55:09 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 18

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

\[ y = \frac {x^{2}}{2}+2 x -3 \ln \left (x \right )+c_1 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 22

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

\[ y(x)\to \frac {x^2}{2}+2 x-3 \log (x)+c_1 \]

✓ Sympy. Time used: 0.250 (sec). Leaf size: 17

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

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