Internal problem ID [14346]
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: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
\[ \boxed {2 y^{\prime } t -y-2 t y^{3} \cos \left (t \right )=0} \]
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 70
dsolve(2*t*diff(y(t),t)-y(t)=2*t*y(t)^3*cos(t),y(t), singsol=all)
\begin{align*} y \left (t \right ) &= \frac {\sqrt {-2 \left (\sin \left (t \right ) t -\frac {c_{1}}{2}+\cos \left (t \right )\right ) t}}{2 \sin \left (t \right ) t +2 \cos \left (t \right )-c_{1}} \\ y \left (t \right ) &= -\frac {\sqrt {-2 \left (\sin \left (t \right ) t -\frac {c_{1}}{2}+\cos \left (t \right )\right ) t}}{2 \sin \left (t \right ) t +2 \cos \left (t \right )-c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.276 (sec). Leaf size: 59
DSolve[2*t*y'[t]-y[t]==2*t*y[t]^3*Cos[t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\frac {\sqrt {t}}{\sqrt {-2 t \sin (t)-2 \cos (t)+c_1}} \\ y(t)\to \frac {\sqrt {t}}{\sqrt {-2 t \sin (t)-2 \cos (t)+c_1}} \\ y(t)\to 0 \\ \end{align*}