66.8.6 problem 17

Internal problem ID [16057]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Review Exercises for chapter 1. page 136
Problem number : 17
Date solved : Thursday, October 02, 2025 at 10:40:19 AM
CAS classification : [`x=_G(y,y')`]

\begin{align*} y^{\prime }&=\left (y-3\right ) \left (\sin \left (y\right ) \sin \left (t \right )+\cos \left (t \right )+1\right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=4 \\ \end{align*}

✗ Maple

ode:=diff(y(t),t) = (y(t)-3)*(sin(y(t))*sin(t)+cos(t)+1); 
ic:=[y(0) = 4]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[t],t]==(y[t]-3)*( Sin[y[t]]*Sin[t]+Cos[t]+1); 
ic={y[0]==4}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq((3 - y(t))*(sin(t)*sin(y(t)) + cos(t) + 1) + Derivative(y(t), t),0) 
ics = {y(0): 4} 
dsolve(ode,func=y(t),ics=ics)
 

NotImplementedError : The given ODE -y(t)*sin(t)*sin(y(t)) - y(t)*cos(t) - y(t) + 3*sin(t)*sin(y(t)) + 3*cos(t) + Derivative(y(t), t) + 3 cannot be solved by the factorable group method