69.6.5 problem 129

Internal problem ID [18048]
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 : 129
Date solved : Thursday, October 02, 2025 at 02:35:59 PM
CAS classification : [_linear]

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

With initial conditions

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

✓ Maple. Time used: 0.023 (sec). Leaf size: 10

ode:=diff(y(x),x)*cos(x)-y(x)*sin(x) = 2*x; 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = x^{2} \sec \left (x \right ) \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 11

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

\begin{align*} y(x)&\to x^2 \sec (x) \end{align*}

✓ Sympy. Time used: 0.460 (sec). Leaf size: 8

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

\[ y{\left (x \right )} = \frac {x^{2}}{\cos {\left (x \right )}} \]