Untitled

249 days ago by jhlee2chn

var('x,y') F(x,y)=x*arcsin(y)-y*e^(arctan(x)) Fx = diff(F(x, y), x) Fy = diff(F(x, y), y) dydx(x, y) = -Fx/Fy print dydx(x,y) 
       
(y*e^arctan(x)/(x^2 + 1) - arcsin(y))/(x/sqrt(-y^2 + 1) - e^arctan(x))
(y*e^arctan(x)/(x^2 + 1) - arcsin(y))/(x/sqrt(-y^2 + 1) - e^arctan(x))
dydx(0,pi/4) 
       
-1/4*pi + arcsin(1/4*pi)
-1/4*pi + arcsin(1/4*pi)
F(0,pi/4) 
       
-1/4*pi
-1/4*pi
integral(sqrt(cos(x))/(sqrt(cos(x))+sqrt(sin(x))), x, 0, pi/2) 
       
integrate(sqrt(cos(x))/(sqrt(sin(x)) + sqrt(cos(x))), x, 0, 1/2*pi)
integrate(sqrt(cos(x))/(sqrt(sin(x)) + sqrt(cos(x))), x, 0, 1/2*pi)
var('x,y') F(x,y)=sqrt(x)+sqrt(y)-1 Fx = diff(F(x, y), x) Fy = diff(F(x, y), y) dydx(x, y) = -Fx/Fy print dydx(x,y) 
       
-sqrt(y)/sqrt(x)
-sqrt(y)/sqrt(x)
var('x') y = function('y', x) de = (cos(y)*sinh(x)+1)*diff(x) - (sin(y)*cosh(x))*diff(y) == 0 desolve(de, [y, x], [1,2], contrib_ode = 'True') 
       
cos(y(x))*cosh(x) + x == cos(2)*cosh(1) + 1
cos(y(x))*cosh(x) + x == cos(2)*cosh(1) + 1