85.5.3 problem 6

Internal problem ID [22449]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 1. Differential equations in general. Section 1.3. B Exercises at page 22
Problem number : 6
Date solved : Thursday, October 02, 2025 at 08:39:42 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y^{p} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 19

ode:=diff(y(x),x) = y(x)^p; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (-x p +c_1 +x \right )^{-\frac {1}{p -1}} \]

✓ Mathematica. Time used: 0.454 (sec). Leaf size: 31

ode=D[y[x],{x,1}]==y[x]^p; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to (-((p-1) (x+c_1))){}^{\frac {1}{1-p}}\\ y(x)&\to 0^{\frac {1}{p}} \end{align*}

✓ Sympy. Time used: 0.191 (sec). Leaf size: 29

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

\[ \left [ y{\left (x \right )} = \begin {cases} \left (- C_{1} p + C_{1} - p x + x\right )^{- \frac {1}{p - 1}} & \text {for}\: p \neq 1 \\\text {NaN} & \text {otherwise} \end {cases}, \ y{\left (x \right )} = \begin {cases} C_{1} e^{x} & \text {for}\: p = 1 \\\text {NaN} & \text {otherwise} \end {cases}\right ] \]