74.7.3 problem 3

Internal problem ID [16080]
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
Date solved : Tuesday, January 28, 2025 at 08:36:55 AM
CAS classification : [_Bernoulli]

\begin{align*} 2 y^{\prime } t -y&=2 t y^{3} \cos \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.179 (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 &= \frac {\sqrt {-2 t \left (t \sin \left (t \right )-\frac {c_{1}}{2}+\cos \left (t \right )\right )}}{2 t \sin \left (t \right )+2 \cos \left (t \right )-c_{1}} \\ y &= -\frac {\sqrt {-2 t \left (t \sin \left (t \right )-\frac {c_{1}}{2}+\cos \left (t \right )\right )}}{2 t \sin \left (t \right )+2 \cos \left (t \right )-c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.280 (sec). Leaf size: 71

DSolve[2*t*D[y[t],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 \int _1^t\cos (K[1]) K[1]dK[1]+c_1}} \\ y(t)\to \frac {\sqrt {t}}{\sqrt {-2 \int _1^t\cos (K[1]) K[1]dK[1]+c_1}} \\ y(t)\to 0 \\ \end{align*}