Internal problem ID [14339]
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: 57.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
\[ \boxed {-y^{2} \sin \left (t y\right )+\left (\cos \left (t y\right )-t y \sin \left (t y\right )\right ) y^{\prime }=-2 t} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 20
dsolve((2*t-y(t)^2*sin(t*y(t)))+(cos(t*y(t))-t*y(t)*sin(t*y(t)))*diff(y(t),t)=0,y(t), singsol=all)
\[ y \left (t \right ) = \frac {\operatorname {RootOf}\left (t^{3}+\textit {\_Z} \cos \left (\textit {\_Z} \right )+c_{1} t \right )}{t} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 43
DSolve[(2*t-y[t]^2*Sin[t*y[t]])+(Cos[t*y[t]]-t*y[t]*Sin[t*y[t]])*y'[x]==0,y[t],t,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\left \{y'(x) (\cos (t y(t))-t y(t) \sin (t y(t)))+y(t)^2 (-\sin (t y(t)))+2 t=0\right \},\{y(t)\}\right ] \]