60.1.272 problem 278

Internal problem ID [10286]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 278
Date solved : Sunday, March 30, 2025 at 03:43:01 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} \left (y^{2}+4 \sin \left (x \right )\right ) y^{\prime }-\cos \left (x \right )&=0 \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 28

ode:=(y(x)^2+4*sin(x))*diff(y(x),x)-cos(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \frac {\left (-8 y^{2}-4 y-32 \sin \left (x \right )-1\right ) {\mathrm e}^{-4 y}}{32}+c_1 = 0 \]

✓ Mathematica. Time used: 0.187 (sec). Leaf size: 83

ode=(y[x]^2+4*Sin[x])*D[y[x],x]-Cos[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^x-e^{-4 y(x)} \cos (K[1])dK[1]+\int _1^{y(x)}\left (e^{-4 K[2]} K[2]^2-e^{-4 K[2]} \left (e^{4 K[2]} \int _1^x4 e^{-4 K[2]} \cos (K[1])dK[1]-4 \sin (x)\right )\right )dK[2]=c_1,y(x)\right ] \]

✓ Sympy. Time used: 1.924 (sec). Leaf size: 36

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((y(x)**2 + 4*sin(x))*Derivative(y(x), x) - cos(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ C_{1} - \frac {\left (- 8 y^{2}{\left (x \right )} - 4 y{\left (x \right )} - 1\right ) e^{- 4 y{\left (x \right )}}}{32} + e^{- 4 y{\left (x \right )}} \sin {\left (x \right )} = 0 \]