14.2.20 problem 22

Internal problem ID [2508]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.4 separable equations. Excercises page 24
Problem number : 22
Date solved : Sunday, March 30, 2025 at 12:05:49 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 1+t -2 y+\left (4 t -3 y-6\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.270 (sec). Leaf size: 56

ode:=1+t-2*y(t)+(4*t-3*y(t)-6)*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {\left (-t +3\right ) {\operatorname {RootOf}\left (-4+\left (3 c_1 \,t^{4}-36 c_1 \,t^{3}+162 c_1 \,t^{2}-324 c_1 t +243 c_1 \right ) \textit {\_Z}^{20}-\textit {\_Z}^{4}\right )}^{4}}{3}-\frac {t}{3}+3 \]

✓ Mathematica. Time used: 60.074 (sec). Leaf size: 1511

ode=(1+t-2*y[t])+(4*t-3*y[t]-6)*D[y[t],t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Sympy. Time used: 1.121 (sec). Leaf size: 36

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t + (4*t - 3*y(t) - 6)*Derivative(y(t), t) - 2*y(t) + 1,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ \log {\left (y{\left (t \right )} - 2 \right )} = C_{1} + \log {\left (\frac {\sqrt [4]{\frac {t - 3}{y{\left (t \right )} - 2} - 1}}{\left (\frac {t - 3}{y{\left (t \right )} - 2} + 3\right )^{\frac {5}{4}}} \right )} \]