8.1.3 problem 3

Internal problem ID [653]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.2. Integrals as general and particular solutions. Page 16
Problem number : 3
Date solved : Tuesday, March 04, 2025 at 11:30:57 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (4\right )&=0 \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 11

ode:=diff(y(x),x) = x^(1/2); 
ic:=y(4) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {2 x^{{3}/{2}}}{3}-\frac {16}{3} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 16

ode=D[y[x],x] == x^(1/2); 
ic=y[4]==0; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {2}{3} \left (x^{3/2}-8\right ) \]

✓ Sympy. Time used: 0.298 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = \frac {2 x^{\frac {3}{2}}}{3} - \frac {16}{3} \]