7.4.28 problem 28

Internal problem ID [100]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.5 (linear equations). Problems at page 54
Problem number : 28
Date solved : Saturday, March 29, 2025 at 04:31:24 PM
CAS classification : [_linear]

\begin{align*} \frac {1+2 x y}{x^{\prime }}&=y^{2}+1 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 25

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

\[ x = \frac {y}{2}+\frac {\arctan \left (y \right ) y^{2}}{2}+\frac {\arctan \left (y \right )}{2}+c_1 \,y^{2}+c_1 \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 30

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

\[ x(y)\to \frac {1}{2} \left (\left (y^2+1\right ) \arctan (y)+2 c_1 y^2+y+2 c_1\right ) \]

✓ Sympy. Time used: 0.441 (sec). Leaf size: 53

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

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