68.6.51 problem 58

Internal problem ID [17361]
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 : 58
Date solved : Thursday, October 02, 2025 at 02:11:14 PM
CAS classification : [_exact]

\begin{align*} -1+{\mathrm e}^{y t} y+y \cos \left (y t \right )+\left (1+{\mathrm e}^{y t} t +t \cos \left (y t \right )\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 27

ode:=-1+exp(t*y(t))*y(t)+y(t)*cos(t*y(t))+(1+exp(t*y(t))*t+t*cos(t*y(t)))*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {\operatorname {RootOf}\left (\sin \left (\textit {\_Z} \right ) t +{\mathrm e}^{\textit {\_Z}} t +c_1 t -t^{2}+\textit {\_Z} \right )}{t} \]

✓ Mathematica. Time used: 0.343 (sec). Leaf size: 107

ode=(-1+Exp[t*y[t]]*y[t]+y[t]*Cos[t*y[t]])+(1+Exp[t*y[t]]*t+t*Cos[t*y[t]])*D[y[t],t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq((t*exp(t*y(t)) + t*cos(t*y(t)) + 1)*Derivative(y(t), t) + y(t)*exp(t*y(t)) + y(t)*cos(t*y(t)) - 1,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

Timed Out