74.6.7 problem 7

Internal problem ID [15959]
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 : 7
Date solved : Monday, March 31, 2025 at 02:16:33 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 21

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

\[ -\frac {\cos \left (2 t \right )}{2 y^{2}}-\frac {2}{3 y^{{3}/{2}}}+c_1 = 0 \]

✓ Mathematica. Time used: 0.325 (sec). Leaf size: 68

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

\[ \text {Solve}\left [\int _1^t\frac {\sin (2 K[1])}{y(t)^2}dK[1]+\int _1^{y(t)}\left (\frac {\cos (2 t)}{K[2]^3}-\int _1^t-\frac {2 \sin (2 K[1])}{K[2]^3}dK[1]+\frac {1}{K[2]^{5/2}}\right )dK[2]=c_1,y(t)\right ] \]

✗ Sympy

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

Timed Out