74.8.17 problem 17

Internal problem ID [16082]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Review exercises, page 80
Problem number : 17
Date solved : Monday, March 31, 2025 at 02:41:07 PM
CAS classification : [_exact]

\begin{align*} t^{2} y+\sin \left (t \right )+\left (\frac {t^{3}}{3}-\cos \left (y\right )\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 21

ode:=t^2*y(t)+sin(t)+(1/3*t^3-cos(y(t)))*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ \frac {t^{3} y}{3}-\cos \left (t \right )-\sin \left (y\right )+c_1 = 0 \]

✓ Mathematica. Time used: 0.209 (sec). Leaf size: 60

ode=(t^2*y[t]+Sin[t])+(1/3*t^3-Cos[y[t]])*D[y[t],t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^{y(t)}\left (t^3-3 \cos (K[2])-\int _1^t3 K[1]^2dK[1]\right )dK[2]+\int _1^t\left (3 y(t) K[1]^2+3 \sin (K[1])\right )dK[1]=c_1,y(t)\right ] \]

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t**2*y(t) + (t**3/3 - cos(y(t)))*Derivative(y(t), t) + sin(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

Timed Out