29.5.21 problem 137
Internal
problem
ID
[4738]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Various
5
Problem
number
:
137
Date
solved
:
Tuesday, March 04, 2025 at 07:12:21 PM
CAS
classification
:
[_linear]
\begin{align*} y^{\prime }&=\sec \left (x \right )^{2}+y \sec \left (x \right ) \operatorname {Csx} \left (x \right ) \end{align*}
✓ Maple. Time used: 0.003 (sec). Leaf size: 32
ode:=diff(y(x),x) = sec(x)^2+y(x)*sec(x)*Csx(x);
dsolve(ode,y(x), singsol=all);
\[
y \left (x \right ) = \left (\int \sec \left (x \right )^{2} {\mathrm e}^{-\int \sec \left (x \right ) \operatorname {Csx} \left (x \right )d x}d x +c_{1} \right ) {\mathrm e}^{\int \sec \left (x \right ) \operatorname {Csx} \left (x \right )d x}
\]
✓ Mathematica. Time used: 0.121 (sec). Leaf size: 57
ode=D[y[x],x]==Sec[x]^2+y[x] Sec[x]Csx[x];
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\[
y(x)\to \exp \left (\int _1^x\text {Csx}(K[1]) \sec (K[1])dK[1]\right ) \left (\int _1^x\exp \left (-\int _1^{K[2]}\text {Csx}(K[1]) \sec (K[1])dK[1]\right ) \sec ^2(K[2])dK[2]+c_1\right )
\]
✓ Sympy. Time used: 27.055 (sec). Leaf size: 85
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(-Csx(x)*y(x)/cos(x) + Derivative(y(x), x) - 1/cos(x)**2,0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
y{\left (x \right )} = \frac {\left (C_{1} + \int \frac {e^{- \int \frac {\operatorname {Csx}{\left (x \right )}}{\cos {\left (x \right )}}\, dx}}{\cos ^{2}{\left (x \right )}}\, dx + \int \frac {\operatorname {Csx}{\left (x \right )} y{\left (x \right )} e^{- \int \frac {\operatorname {Csx}{\left (x \right )}}{\cos {\left (x \right )}}\, dx}}{\cos {\left (x \right )}}\, dx\right ) e^{\int \frac {\operatorname {Csx}{\left (x \right )}}{\cos {\left (x \right )}}\, dx}}{\left (e^{\int \frac {\operatorname {Csx}{\left (x \right )}}{\cos {\left (x \right )}}\, dx}\right ) \int \frac {\operatorname {Csx}{\left (x \right )} e^{- \int \frac {\operatorname {Csx}{\left (x \right )}}{\cos {\left (x \right )}}\, dx}}{\cos {\left (x \right )}}\, dx + 1}
\]