74.6.23 problem 24

Internal problem ID [16046]
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 : 24
Date solved : Tuesday, January 28, 2025 at 08:29:03 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: 0.061 (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: 0.279 (sec). Leaf size: 89

DSolve[(2*t-y[t]^2*Sin[t*y[t]])+(Cos[t*y[t]]-t*y[t]*Sin[t*y[t]])*D[y[t],t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^t\left (2 K[1]-\sin (K[1] y(t)) y(t)^2\right )dK[1]+\int _1^{y(t)}\left (\cos (t K[2])-t K[2] \sin (t K[2])-\int _1^t\left (-\cos (K[1] K[2]) K[1] K[2]^2-2 \sin (K[1] K[2]) K[2]\right )dK[1]\right )dK[2]=c_1,y(t)\right ] \]