68.7.35 problem 35

Internal problem ID [17399]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number : 35
Date solved : Thursday, October 02, 2025 at 02:16:53 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} y^{\prime }&=\frac {4 y^{2}-t^{2}}{2 y t} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.084 (sec). Leaf size: 16

ode:=diff(y(t),t) = 1/2*(4*y(t)^2-t^2)/t/y(t); 
ic:=[y(1) = 1]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = \frac {\sqrt {2 t^{2}+2}\, t}{2} \]

✓ Mathematica. Time used: 0.406 (sec). Leaf size: 22

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

\begin{align*} y(t)&\to \frac {\sqrt {t^4+t^2}}{\sqrt {2}} \end{align*}

✓ Sympy. Time used: 0.298 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(Derivative(y(t), t) - (-t**2 + 4*y(t)**2)/(2*t*y(t)),0) 
ics = {y(1): 1} 
dsolve(ode,func=y(t),ics=ics)
 

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