Internal problem ID [14311]
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: 23.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {-2 t y^{2} \sin \left (t^{2}\right )+2 y \cos \left (t^{2}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 40
dsolve(-2*t*y(t)^2*sin(t^2)+2*y(t)*cos(t^2)*diff(y(t),t)=0,y(t), singsol=all)
\begin{align*} y \left (t \right ) &= 0 \\ y \left (t \right ) &= \sec \left (t^{2}\right ) \sqrt {-\cos \left (t^{2}\right ) c_{1}} \\ y \left (t \right ) &= -\sec \left (t^{2}\right ) \sqrt {-\cos \left (t^{2}\right ) c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.057 (sec). Leaf size: 26
DSolve[-2*t*y[t]^2*Sin[t^2]+2*y[t]*Cos[t^2]*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 0 \\ y(t)\to \frac {c_1}{\sqrt {\cos \left (t^2\right )}} \\ y(t)\to 0 \\ \end{align*}