4.3.12 problem 16

Internal problem ID [1177]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.4. Page 76
Problem number : 16
Date solved : Tuesday, September 30, 2025 at 04:27:28 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {t^{2}}{\left (t^{3}+1\right ) y} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 39

ode:=diff(y(t),t) = t^2/(t^3+1)/y(t); 
dsolve(ode,y(t), singsol=all);
 

\begin{align*} y &= -\frac {\sqrt {6 \ln \left (t^{3}+1\right )+9 c_1}}{3} \\ y &= \frac {\sqrt {6 \ln \left (t^{3}+1\right )+9 c_1}}{3} \\ \end{align*}

✓ Mathematica. Time used: 0.062 (sec). Leaf size: 56

ode=D[y[t],t] == t^2/(t^3+1)/y[t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -\sqrt {\frac {2}{3}} \sqrt {\log \left (t^3+1\right )+3 c_1}\\ y(t)&\to \sqrt {\frac {2}{3}} \sqrt {\log \left (t^3+1\right )+3 c_1} \end{align*}

✓ Sympy. Time used: 0.213 (sec). Leaf size: 36

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t**2/((t**3 + 1)*y(t)) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ \left [ y{\left (t \right )} = - \frac {\sqrt {C_{1} + 6 \log {\left (t^{3} + 1 \right )}}}{3}, \ y{\left (t \right )} = \frac {\sqrt {C_{1} + 6 \log {\left (t^{3} + 1 \right )}}}{3}\right ] \]