74.6.50 problem 57

Internal problem ID [16073]
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
Date solved : Tuesday, January 28, 2025 at 08:35:23 AM
CAS classification : [_exact]

\begin{align*} 2 t -y^{2} \sin \left (t y\right )+\left (\cos \left (t y\right )-t y \sin \left (t y\right )\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.056 (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)
 

\[ y = \frac {\operatorname {RootOf}\left (t^{3}+\textit {\_Z} \cos \left (\textit {\_Z} \right )+c_{1} t \right )}{t} \]

✓ Solution by Mathematica

Time used: 0.014 (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]])*D[y[x],x]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\left \{y''(x) (\cos (t y(t))-t y(t) \sin (t y(t)))+y(t)^2 (-\sin (t y(t)))+2 t=0\right \},\{y(t)\}\right ] \]