30.5.29 problem 29

Internal problem ID [7528]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.6, Substitutions and Transformations. Exercises. page 76
Problem number : 29
Date solved : Tuesday, September 30, 2025 at 04:42:07 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} x +y-1+\left (y-x -5\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 32

ode:=x+y(x)-1+(y(x)-x-5)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = 3+\tan \left (\operatorname {RootOf}\left (2 \textit {\_Z} +\ln \left (\sec \left (\textit {\_Z} \right )^{2}\right )+2 \ln \left (x +2\right )+2 c_1 \right )\right ) \left (-x -2\right ) \]

✓ Mathematica. Time used: 0.032 (sec). Leaf size: 59

ode=(x+y[x]-1)+(y[x]-x-5)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [2 \arctan \left (1-\frac {2 (x+2)}{-y(x)+x+5}\right )+\log \left (\frac {x^2+y(x)^2-6 y(x)+4 x+13}{2 (x+2)^2}\right )+2 \log (x+2)+c_1=0,y(x)\right ] \]

✓ Sympy. Time used: 2.114 (sec). Leaf size: 34

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x + (-x + y(x) - 5)*Derivative(y(x), x) + y(x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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