71.4.11 problem 11

Internal problem ID [14312]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.2, page 53
Problem number : 11
Date solved : Monday, March 31, 2025 at 12:16:59 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=\sqrt {\frac {y-4}{x}} \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 38

ode:=diff(y(x),x) = ((y(x)-4)/x)^(1/2); 
dsolve(ode,y(x), singsol=all);
 

\[ -\ln \left (\frac {-y+4+x}{x}\right )+2 \,\operatorname {arctanh}\left (\sqrt {\frac {y-4}{x}}\right )-\ln \left (x \right )-c_1 = 0 \]

✓ Mathematica. Time used: 0.16 (sec). Leaf size: 29

ode=D[y[x],x]==Sqrt[ (y[x]-4)/x ]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to x+c_1 \sqrt {x}+4+\frac {c_1{}^2}{4} \\ y(x)\to 4 \\ \end{align*}

✓ Sympy. Time used: 3.954 (sec). Leaf size: 92

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-sqrt((y(x) - 4)/x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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