76.3.15 problem 15

Internal problem ID [17315]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.4 (Differences between linear and nonlinear equations). Problems at page 79
Problem number : 15
Date solved : Monday, March 31, 2025 at 03:52:04 PM
CAS classification : [_separable]

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

With initial conditions

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

✗ Maple

ode:=diff(y(t),t) = -4*t/y(t); 
ic:=y(0) = y__0; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ \text {No solution found} \]

✓ Mathematica. Time used: 0.084 (sec). Leaf size: 37

ode=D[y[t],t]==-4*t/y[t]; 
ic={y[0]==y0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)\to -\sqrt {\text {y0}^2-4 t^2} \\ y(t)\to \sqrt {\text {y0}^2-4 t^2} \\ \end{align*}

✓ Sympy. Time used: 0.288 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(4*t/y(t) + Derivative(y(t), t),0) 
ics = {y(0): y__0} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \sqrt {- 4 t^{2} + \left (y^{0}\right )^{2}} \]