Internal problem ID [14332]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y \left (2 \,{\mathrm e}^{t}+4 t \right )+3 \left ({\mathrm e}^{t}+t^{2}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (t \right ) = \frac {c_{1}}{\left ({\mathrm e}^{t}+t^{2}\right )^{\frac {2}{3}}} \]
✓ Solution by Mathematica
Time used: 0.084 (sec). Leaf size: 24
DSolve[y[t]*(2*Exp[t]+4*t)+3*(Exp[t]+t^2)*y'[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*}