69.6.7 problem 131

Internal problem ID [18050]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page 54
Problem number : 131
Date solved : Thursday, October 02, 2025 at 02:36:03 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }-y \tan \left (x \right )&=\frac {1}{\cos \left (x \right )^{3}} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.018 (sec). Leaf size: 9

ode:=diff(y(x),x)-y(x)*tan(x) = 1/cos(x)^3; 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \sec \left (x \right ) \tan \left (x \right ) \]

✓ Mathematica. Time used: 0.032 (sec). Leaf size: 10

ode=D[y[x],x]-y[x]*Tan[x]==1/Cos[x]^3; 
ic={y[0]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \tan (x) \sec (x) \end{align*}

✓ Sympy. Time used: 1.427 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x)*tan(x) + Derivative(y(x), x) - 1/cos(x)**3,0) 
ics = {y(0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {\tan {\left (x \right )}}{\cos {\left (x \right )}} \]