90.3.12 problem 12

Internal problem ID [25076]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 41
Problem number : 12
Date solved : Thursday, October 02, 2025 at 11:49:23 PM
CAS classification : [_separable]

\begin{align*} y^{3} y^{\prime }&=t \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 57

ode:=y(t)^3*diff(y(t),t) = t; 
dsolve(ode,y(t), singsol=all);
 

\begin{align*} y &= \left (2 t^{2}+c_1 \right )^{{1}/{4}} \\ y &= -\left (2 t^{2}+c_1 \right )^{{1}/{4}} \\ y &= -i \left (2 t^{2}+c_1 \right )^{{1}/{4}} \\ y &= i \left (2 t^{2}+c_1 \right )^{{1}/{4}} \\ \end{align*}

✓ Mathematica. Time used: 0.107 (sec). Leaf size: 96

ode=y[t]^3*D[y[t],{t,1}]==t; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -\sqrt [4]{2} \sqrt [4]{t^2+2 c_1}\\ y(t)&\to -i \sqrt [4]{2} \sqrt [4]{t^2+2 c_1}\\ y(t)&\to i \sqrt [4]{2} \sqrt [4]{t^2+2 c_1}\\ y(t)&\to \sqrt [4]{2} \sqrt [4]{t^2+2 c_1} \end{align*}

✓ Sympy. Time used: 0.735 (sec). Leaf size: 54

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

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