15.1.27 problem 27

Internal problem ID [2867]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 5, page 21
Problem number : 27
Date solved : Sunday, March 30, 2025 at 12:35:11 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (2\right )&=0 \end{align*}

✓ Maple. Time used: 0.094 (sec). Leaf size: 17

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

\[ y = \tan \left (\frac {1}{5} x^{5}-\frac {1}{4} x^{4}-\frac {12}{5}\right ) \]

✓ Mathematica. Time used: 0.367 (sec). Leaf size: 22

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

\[ y(x)\to \tan \left (\frac {1}{20} \left (4 x^5-5 x^4-48\right )\right ) \]

✓ Sympy. Time used: 0.728 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = - \tan {\left (- \frac {x^{5}}{5} + \frac {x^{4}}{4} + \frac {12}{5} \right )} \]