17.1.2 problem 1(b)

Internal problem ID [4092]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 2. First order equations. Exercises at page 14
Problem number : 1(b)
Date solved : Tuesday, September 30, 2025 at 07:02:32 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=1-x^{5}+\sqrt {x} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

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

\[ y = \frac {2 x^{{3}/{2}}}{3}-\frac {x^{6}}{6}+x +c_1 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 25

ode=D[y[x],x]==1-x^5+Sqrt[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {2 x^{3/2}}{3}-\frac {x^6}{6}+x+c_1 \end{align*}

✓ Sympy. Time used: 0.160 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-sqrt(x) + x**5 + Derivative(y(x), x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + \frac {2 x^{\frac {3}{2}}}{3} - \frac {x^{6}}{6} + x \]