84.2.8 problem 1.13

Internal problem ID [22077]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 1. Basic concepts. Supplementary problems
Problem number : 1.13
Date solved : Thursday, October 02, 2025 at 08:23:33 PM
CAS classification : [_quadrature]

\begin{align*} {b^{\prime }}^{7}&=3 p \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 170

ode:=diff(b(p),p)^7 = 3*p; 
dsolve(ode,b(p), singsol=all);
 

\begin{align*} b &= \frac {7 p^{{8}/{7}} 3^{{1}/{7}}}{8}+c_1 \\ b &= -\frac {7 \left (i \sin \left (\frac {2 \pi }{7}\right )-\cos \left (\frac {2 \pi }{7}\right )\right ) 3^{{1}/{7}} p^{{8}/{7}}}{8}+c_1 \\ b &= \frac {7 \,3^{{1}/{7}} \left (i \sin \left (\frac {2 \pi }{7}\right )+\cos \left (\frac {2 \pi }{7}\right )\right ) p^{{8}/{7}}}{8}+c_1 \\ b &= c_1 -\frac {7 p^{{8}/{7}} 3^{{1}/{7}} \left (\cos \left (\frac {3 \pi }{7}\right )+i \sin \left (\frac {3 \pi }{7}\right )\right )}{8} \\ b &= \frac {7 p^{{8}/{7}} 3^{{1}/{7}} \left (-\cos \left (\frac {3 \pi }{7}\right )+i \sin \left (\frac {3 \pi }{7}\right )\right )}{8}+c_1 \\ b &= \frac {7 p^{{8}/{7}} 3^{{1}/{7}} \left (i \sin \left (\frac {\pi }{7}\right )-\cos \left (\frac {\pi }{7}\right )\right )}{8}+c_1 \\ b &= c_1 -\frac {7 p^{{8}/{7}} 3^{{1}/{7}} \left (i \sin \left (\frac {\pi }{7}\right )+\cos \left (\frac {\pi }{7}\right )\right )}{8} \\ \end{align*}

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 173

ode=D[b[p],p]^7==3*p; 
ic={}; 
DSolve[{ode,ic},b[p],p,IncludeSingularSolutions->True]
 

\begin{align*} b(p)&\to -\frac {7}{8} \sqrt [7]{-3} p^{8/7}+c_1\\ b(p)&\to \frac {7}{8} \sqrt [7]{3} p^{8/7}+c_1\\ b(p)&\to \frac {7}{8} (-1)^{2/7} \sqrt [7]{3} p^{8/7}+c_1\\ b(p)&\to -\frac {7}{8} (-1)^{3/7} \sqrt [7]{3} p^{8/7}+c_1\\ b(p)&\to \frac {7}{8} (-1)^{4/7} \sqrt [7]{3} p^{8/7}+c_1\\ b(p)&\to -\frac {7}{8} (-1)^{5/7} \sqrt [7]{3} p^{8/7}+c_1\\ b(p)&\to \frac {7}{8} (-1)^{6/7} \sqrt [7]{3} p^{8/7}+c_1 \end{align*}

✗ Sympy

from sympy import * 
p = symbols("p") 
b = Function("b") 
ode = Eq(-3*p + Derivative(b(p), p)**7,0) 
ics = {} 
dsolve(ode,func=b(p),ics=ics)
 

Timed Out