66.1.9 problem 12

Internal problem ID [15896]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.2. page 33
Problem number : 12
Date solved : Thursday, October 02, 2025 at 10:29:22 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

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

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

✓ Mathematica. Time used: 0.052 (sec). Leaf size: 35

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

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

✓ Sympy. Time used: 0.132 (sec). Leaf size: 22

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

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