73.5.23 problem 6.7 (k)

Internal problem ID [15063]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 6. Simplifying through simplifiction. Additional exercises. page 114
Problem number : 6.7 (k)
Date solved : Monday, March 31, 2025 at 01:20:38 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Maple. Time used: 0.022 (sec). Leaf size: 25

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

\[ -\frac {y+x}{\sqrt {x \left (y+x \right )}}+\frac {\ln \left (x \right )}{2}-c_1 = 0 \]

✓ Mathematica. Time used: 0.211 (sec). Leaf size: 26

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

\[ y(x)\to \frac {1}{4} x \left (\log ^2(x)+2 c_1 \log (x)-4+c_1{}^2\right ) \]

✓ Sympy. Time used: 0.886 (sec). Leaf size: 27

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

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