68.6.43 problem 49

Internal problem ID [17353]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.4, page 57
Problem number : 49
Date solved : Thursday, October 02, 2025 at 02:10:13 PM
CAS classification : [_separable]

\begin{align*} y \left (2 \,{\mathrm e}^{t}+4 t \right )+3 \left ({\mathrm e}^{t}+t^{2}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

ode:=y(t)*(2*exp(t)+4*t)+3*(exp(t)+t^2)*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {c_1}{\left ({\mathrm e}^{t}+t^{2}\right )^{{2}/{3}}} \]

✓ Mathematica. Time used: 0.116 (sec). Leaf size: 24

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

\begin{align*} y(t)&\to \frac {c_1}{\left (t^2+e^t\right )^{2/3}}\\ y(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.197 (sec). Leaf size: 14

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

\[ y{\left (t \right )} = \frac {C_{1}}{\left (t^{2} + e^{t}\right )^{\frac {2}{3}}} \]