71.1.17 problem 32 (page 40)

Internal problem ID [19193]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 32 (page 40)
Date solved : Thursday, October 02, 2025 at 03:42:56 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 18

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

\[ y = \frac {\left (2 c_1 +x \right ) \sec \left (x \right )}{2}+\frac {\sin \left (x \right )}{2} \]

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 23

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

\begin{align*} y(x)&\to \sec (x) \left (\int _1^x\cos ^2(K[1])dK[1]+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.557 (sec). Leaf size: 17

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

\[ y{\left (x \right )} = \frac {C_{1} + \frac {x}{2} + \frac {\sin {\left (2 x \right )}}{4}}{\cos {\left (x \right )}} \]