38.2.33 problem 33

Internal problem ID [6462]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 24. First order differential equations. Further problems 24. page 1068
Problem number : 33
Date solved : Wednesday, March 05, 2025 at 12:48:50 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

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

\[ y = \sqrt {x^{2}+1}\, c_1 -1 \]

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 24

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

\begin{align*} y(x)\to -1+c_1 \sqrt {x^2+1} \\ y(x)\to -1 \\ \end{align*}

✓ Sympy. Time used: 0.267 (sec). Leaf size: 14

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

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