74.7.41 problem 41

Internal problem ID [16047]
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 : 41
Date solved : Monday, March 31, 2025 at 02:36:39 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} y^{4}+\left (t^{4}-t y^{3}\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=2 \end{align*}

✓ Maple. Time used: 1.606 (sec). Leaf size: 105

ode:=y(t)^4+(t^4-t*y(t)^3)*diff(y(t),t) = 0; 
ic:=y(1) = 2; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = \frac {{\mathrm e}^{-\operatorname {RootOf}\left (6 i \pi \_Z8 +\operatorname {LambertW}\left (\_Z10 , -{\mathrm e}^{-3 \textit {\_Z}}\right )+3 \textit {\_Z} +3 \ln \left (2\right )+6 i \pi \_Z11 \right )}}{\left (-\frac {{\mathrm e}^{-3 \operatorname {RootOf}\left (6 i \pi \_Z8 +\operatorname {LambertW}\left (\_Z10 , -{\mathrm e}^{-3 \textit {\_Z}}\right )+3 \textit {\_Z} +3 \ln \left (2\right )+6 i \pi \_Z11 \right )}}{t^{3} \operatorname {LambertW}\left (\_Z10 , -\frac {{\mathrm e}^{-3 \operatorname {RootOf}\left (6 i \pi \_Z8 +\operatorname {LambertW}\left (\_Z10 , -{\mathrm e}^{-3 \textit {\_Z}}\right )+3 \textit {\_Z} +3 \ln \left (2\right )+6 i \pi \_Z11 \right )}}{t^{3}}\right )}\right )^{{1}/{3}}} \]

✗ Mathematica

ode=y[t]^4+(t^4-t*y[t]^3)*D[y[t],t]==0; 
ic={y[1]==2}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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✓ Sympy. Time used: 1.408 (sec). Leaf size: 20

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq((t**4 - t*y(t)**3)*Derivative(y(t), t) + y(t)**4,0) 
ics = {y(1): 2} 
dsolve(ode,func=y(t),ics=ics)
 

\[ \log {\left (y{\left (t \right )} \right )} = - \frac {8}{3} + \log {\left (2 \right )} + \frac {y^{3}{\left (t \right )}}{3 t^{3}} \]