60.2.419 problem 997

Internal problem ID [10993]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 997
Date solved : Wednesday, March 05, 2025 at 01:35:50 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 16

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

\[ y = -\cos \left (x \right )+\frac {1}{-x +c_{1}} \]

✓ Mathematica. Time used: 0.172 (sec). Leaf size: 26

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

\begin{align*} y(x)\to -\cos (x)+\frac {1}{-x+c_1} \\ y(x)\to -\cos (x) \\ \end{align*}

✓ Sympy. Time used: 1.180 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = - \frac {C_{1} \cos {\left (x \right )} + x \cos {\left (x \right )} + 1}{C_{1} + x} \]