Internal problem ID [14347]
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: 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class D`], _Bernoulli]
\[ \boxed {y^{\prime } t -y-y^{3} \sin \left (t \right ) t=0} \]
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 52
dsolve(t*diff(y(t),t)-y(t)=t*y(t)^3*sin(t),y(t), singsol=all)
\begin{align*} y \left (t \right ) &= \frac {t}{\sqrt {2 t^{2} \cos \left (t \right )-4 \cos \left (t \right )-4 \sin \left (t \right ) t +c_{1}}} \\ y \left (t \right ) &= -\frac {t}{\sqrt {2 t^{2} \cos \left (t \right )-4 \cos \left (t \right )-4 \sin \left (t \right ) t +c_{1}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.335 (sec). Leaf size: 61
DSolve[t*y'[t]-y[t]==t*y[t]^3*Sin[t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\frac {t}{\sqrt {2 \left (t^2-2\right ) \cos (t)-4 t \sin (t)+c_1}} \\ y(t)\to \frac {t}{\sqrt {2 \left (t^2-2\right ) \cos (t)-4 t \sin (t)+c_1}} \\ y(t)\to 0 \\ \end{align*}