74.6.43 problem 49

Internal problem ID [16066]
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 : Tuesday, January 28, 2025 at 08:35:07 AM
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*}

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.192 (sec). Leaf size: 24

DSolve[y[t]*(2*Exp[t]+4*t)+3*(Exp[t]+t^2)*D[y[t],t]==0,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*}