30.5.24 problem 24

Internal problem ID [7523]
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 : 24
Date solved : Tuesday, September 30, 2025 at 04:41:55 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]

\begin{align*} y^{\prime }+\frac {y}{x -2}&=5 \left (x -2\right ) \sqrt {y} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 25

ode:=diff(y(x),x)+y(x)/(x-2) = 5*(x-2)*y(x)^(1/2); 
dsolve(ode,y(x), singsol=all);
 

\[ \sqrt {y}-x^{2}+4 x -4-\frac {c_1}{\sqrt {x -2}} = 0 \]

✓ Mathematica. Time used: 0.19 (sec). Leaf size: 81

ode=D[y[x],x]+y[x]/(x-2)==5*(x-2)*Sqrt[ y[x] ]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x^5-10 x^4+40 x^3-2 x^2 \left (40+c_1 \sqrt {2-x}\right )+8 x \left (10+c_1 \sqrt {2-x}\right )-8 c_1 \sqrt {2-x}-32-c_1{}^2}{x-2} \end{align*}

✓ Sympy. Time used: 2.145 (sec). Leaf size: 748

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-(5*x - 10)*sqrt(y(x)) + Derivative(y(x), x) + y(x)/(x - 2),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \text {Solution too large to show} \]