38.2.30 problem 30

Internal problem ID [6459]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 24. First order differential equations. Further problems 24. page 1068
Problem number : 30
Date solved : Sunday, March 30, 2025 at 11:02:04 AM
CAS classification : [_separable]

\begin{align*} y+\left (x^{2}-4 x \right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

ode:=y(x)+(x^2-4*x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \,x^{{1}/{4}}}{\left (x -4\right )^{{1}/{4}}} \]

✓ Mathematica. Time used: 0.042 (sec). Leaf size: 27

ode=y[x]+(x^2-4*x)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {c_1 \sqrt [4]{x}}{\sqrt [4]{4-x}} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.248 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x**2 - 4*x)*Derivative(y(x), x) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} \sqrt [4]{x}}{\sqrt [4]{x - 4}} \]