restart;
interface(version);
SWRwU3RhbmRhcmR+V29ya3NoZWV0fkludGVyZmFjZSx+TWFwbGV+MjAyMS4yLH5XaW5kb3dzfjEwLH5Ob3ZlbWJlcn4yM34yMDIxfkJ1aWxkfklEfjE1NzYzNDlHNiI=
infolevel[dsolve]:=2; ode:=(tan(x)*sec(x)-2*y(x))*diff(y(x),x)+sec(x)*(1+2*y(x)*sin(x)) = 0; dsolve(ode,y(x), singsol=all)
LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkqaW5mb2xldmVsR0YnNiNJJ2Rzb2x2ZUdGJSIiIzcjRjE=
LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRvZGVHRigvLCYqJiwmKiYtSSR0YW5HRiU2I0kieEdGKCIiIi1JJHNlY0dGJUY1RjdGNy1JInlHRihGNSEiI0Y3LUklZGlmZkdGJjYkRjpGNkY3RjcqJkY4RjcsJkY3RjcqJkY6RjctSSRzaW5HRiVGNUY3IiIjRjdGNyIiITcjRi4=
Methods for first order ODEs:
--- Trying classification methods ---
trying a quadrature
trying 1st order linear
trying Bernoulli
trying separable
trying inverse linear
trying homogeneous types:
trying Chini
differential order: 1; looking for linear symmetries
trying exact
trying Abel
Looking for potential symmetries
Looking for potential symmetries
Looking for potential symmetries
trying inverse_Riccati
trying an equivalence to an Abel ODE
differential order: 1; trying a linearization to 2nd order
--- trying a change of variables {x -> y(x), y(x) -> x}
differential order: 1; trying a linearization to 2nd order
trying 1st order ODE linearizable_by_differentiation
--- Trying Lie symmetry methods, 1st order ---
-> Computing symmetries using: way = 3
-> Computing symmetries using: way = 4
-> Computing symmetries using: way = 2
trying symmetry patterns for 1st order ODEs
-> trying a symmetry pattern of the form [F(x)*G(y), 0]
-> trying a symmetry pattern of the form [0, F(x)*G(y)]
-> trying symmetry patterns of the forms [F(x),G(y)] and [G(y),F(x)]
-> Computing symmetries using: way = HINT
-> Calling odsolve with the ODE diff(y(x) x) = -y(x)*(sin(x)*tan(x)+cos(x))/sin(x) y(x)
*** Sublevel 2 ***
Methods for first order ODEs:
--- Trying classification methods ---
trying a quadrature
trying 1st order linear
<- 1st order linear successful
-> Calling odsolve with the ODE diff(y(x) x) = y(x)*(1+tan(x)^2)/tan(x) y(x)
*** Sublevel 2 ***
Methods for first order ODEs:
--- Trying classification methods ---
trying a quadrature
trying 1st order linear
<- 1st order linear successful
-> Calling odsolve with the ODE diff(y(x) x) y(x)
*** Sublevel 2 ***
Methods for first order ODEs:
--- Trying classification methods ---
trying a quadrature
trying 1st order linear
<- 1st order linear successful
-> Calling odsolve with the ODE diff(y(x) x)+2*K[1] y(x)
*** Sublevel 2 ***
Methods for first order ODEs:
--- Trying classification methods ---
trying a quadrature
trying 1st order linear
<- 1st order linear successful
-> Calling odsolve with the ODE diff(y(x) x)+y(x)/x y(x)
*** Sublevel 2 ***
Methods for first order ODEs:
--- Trying classification methods ---
trying a quadrature
trying 1st order linear
<- 1st order linear successful
-> Calling odsolve with the ODE diff(y(x) x)-(-2*K[1]*x+y(x))/x y(x)
*** Sublevel 2 ***
Methods for first order ODEs:
--- Trying classification methods ---
trying a quadrature
trying 1st order linear
<- 1st order linear successful
-> Calling odsolve with the ODE diff(y(x) x)-y(x)/x y(x)
*** Sublevel 2 ***
Methods for first order ODEs:
--- Trying classification methods ---
trying a quadrature
trying 1st order linear
<- 1st order linear successful
-> Calling odsolve with the ODE diff(y(x) x)-K[1] y(x)
*** Sublevel 2 ***
Methods for first order ODEs:
--- Trying classification methods ---
trying a quadrature
trying 1st order linear
<- 1st order linear successful
-> Calling odsolve with the ODE diff(y(x) x)+(-K[1]*x+y(x))/x y(x)
*** Sublevel 2 ***
Methods for first order ODEs:
--- Trying classification methods ---
trying a quadrature
trying 1st order linear
<- 1st order linear successful
-> Calling odsolve with the ODE diff(y(x) x) = 0 y(x)
*** Sublevel 2 ***
Methods for first order ODEs:
--- Trying classification methods ---
trying a quadrature
trying 1st order linear
<- 1st order linear successful
-> Calling odsolve with the ODE diff(y(x) x) = y(x)/x y(x)
*** Sublevel 2 ***
Methods for first order ODEs:
--- Trying classification methods ---
trying a quadrature
trying 1st order linear
<- 1st order linear successful
-> Calling odsolve with the ODE diff(y(x) x)+y(x)*(sin(x)*tan(x)+cos(x))/sin(x) y(x)
*** Sublevel 2 ***
Methods for first order ODEs:
--- Trying classification methods ---
trying a quadrature
trying 1st order linear
<- 1st order linear successful
-> Calling odsolve with the ODE diff(y(x) x)+(2*sin(x)*tan(x)*sec(x)*K[1]-tan(x)^2*sec(x)*y(x)-sec(x)*y(x)+2*K[1])/(tan(x)*sec(x)) y(x)
*** Sublevel 2 ***
Methods for first order ODEs:
--- Trying classification methods ---
trying a quadrature
trying 1st order linear
<- 1st order linear successful
-> Calling odsolve with the ODE diff(y(x) x)-y(x)*(tan(x)^2*sec(x)*sin(x)-tan(x)*sec(x)*cos(x)+sec(x)*sin(x)+tan(x))/(sin(x)*tan(x)*sec(x)-1) y(x)
*** Sublevel 2 ***
Methods for first order ODEs:
--- Trying classification methods ---
trying a quadrature
trying 1st order linear
<- 1st order linear successful
-> Calling odsolve with the ODE diff(y(x) x)-(y(x)*tan(x)^2+tan(x)*K[1]+y(x))/tan(x) y(x)
*** Sublevel 2 ***
Methods for first order ODEs:
--- Trying classification methods ---
trying a quadrature
trying 1st order linear
<- 1st order linear successful
-> Calling odsolve with the ODE diff(y(x) x)+(y(x)*sin(x)*tan(x)-sin(x)*K[1]+y(x)*cos(x))/sin(x) y(x)
*** Sublevel 2 ***
Methods for first order ODEs:
--- Trying classification methods ---
trying a quadrature
trying 1st order linear
<- 1st order linear successful
-> Calling odsolve with the ODE diff(y(x) x)-(y(x)*sec(x)*sin(x)*tan(x)^2-y(x)*sec(x)*tan(x)*cos(x)+y(x)*sec(x)*sin(x)+y(x)*tan(x)-2*K[1])/(sin(x)*tan(x)*sec(x)-1) y(x)
*** Sublevel 2 ***
Methods for first order ODEs:
--- Trying classification methods ---
trying a quadrature
trying 1st order linear
<- 1st order linear successful
-> Computing symmetries using: way = HINT
-> Calling odsolve with the ODE diff(y(x) x)-(1/2)/x y(x)
*** Sublevel 2 ***
Methods for first order ODEs:
--- Trying classification methods ---
trying a quadrature
<- quadrature successful
-> Calling odsolve with the ODE diff(y(x) x)+(1/2)*(2*y(x)-1)/x y(x)
*** Sublevel 2 ***
Methods for first order ODEs:
--- Trying classification methods ---
trying a quadrature
trying 1st order linear
<- 1st order linear successful
-> trying a symmetry pattern of the form [F(x),G(x)]
-> trying a symmetry pattern of the form [F(y),G(y)]
-> trying a symmetry pattern of the form [F(x)+G(y), 0]
-> trying a symmetry pattern of the form [0, F(x)+G(y)]
-> trying a symmetry pattern of the form [F(x),G(x)*y+H(x)]
-> trying a symmetry pattern of conformal type
infolevel[dsolve]:=2; dsolve(ode,y(x), singsol=all)
LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkqaW5mb2xldmVsR0YnNiNJJ2Rzb2x2ZUdGJSIiIzcjRjE=
Methods for first order ODEs:
--- Trying classification methods ---
trying a quadrature
trying 1st order linear
trying Bernoulli
trying separable
trying inverse linear
trying homogeneous types:
trying Chini
differential order: 1; looking for linear symmetries
trying exact
trying Abel
trying inverse_Riccati
differential order: 1; trying a linearization to 2nd order
--- trying a change of variables {x -> y(x), y(x) -> x}
differential order: 1; trying a linearization to 2nd order
trying 1st order ODE linearizable_by_differentiation
--- Trying Lie symmetry methods, 1st order ---
-> Computing symmetries using: way = 3
-> Computing symmetries using: way = 4
-> Computing symmetries using: way = 2
trying symmetry patterns for 1st order ODEs
-> trying a symmetry pattern of the form [F(x)*G(y), 0]
-> trying a symmetry pattern of the form [0, F(x)*G(y)]
-> trying symmetry patterns of the forms [F(x),G(y)] and [G(y),F(x)]
-> trying a symmetry pattern of the form [F(x),G(x)]
-> trying a symmetry pattern of the form [F(y),G(y)]
-> trying a symmetry pattern of the form [F(x)+G(y), 0]
-> trying a symmetry pattern of the form [0, F(x)+G(y)]
-> trying a symmetry pattern of the form [F(x),G(x)*y+H(x)]
-> trying a symmetry pattern of conformal type