10.3.9 problem 13

Internal problem ID [1174]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.4. Page 76
Problem number : 13
Date solved : Saturday, March 29, 2025 at 10:44:30 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=-\frac {4 t}{y} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 27

ode:=diff(y(t),t) = -4*t/y(t); 
dsolve(ode,y(t), singsol=all);
 

\begin{align*} y &= \sqrt {-4 t^{2}+c_1} \\ y &= -\sqrt {-4 t^{2}+c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.071 (sec). Leaf size: 46

ode=D[y[t],t]== -4*t/y[t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)\to -\sqrt {2} \sqrt {-2 t^2+c_1} \\ y(t)\to \sqrt {2} \sqrt {-2 t^2+c_1} \\ \end{align*}

✓ Sympy. Time used: 0.234 (sec). Leaf size: 26

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

\[ \left [ y{\left (t \right )} = - \sqrt {C_{1} - 4 t^{2}}, \ y{\left (t \right )} = \sqrt {C_{1} - 4 t^{2}}\right ] \]