`dy/dx + Py = Q ` অবকল সমীকরণের সমাকল গুণক -

Linear differental equation of the form dy/dx + Py = Q where P, Q are functions of x or costants and the coefficient of dy/dx = 1 . Taking e^(int P dx) as Integrating factor the above form reduces to d/dx(ye^(int Pdx))= Qe ^(intPdx). Solution of the equation dy/dx + 2 y tan x = x sin x given y = 0 when x = pi/3 is -

Linear differental equation of the form dy/dx + Py = Q where P, Q are functions of x or costants and the coefficient of dy/dx = 1 . Taking e^(int P dx) as Integrating factor the above form reduces to d/dx(ye^(int Pdx))= Qe ^(intPdx). Solution of the equation cos t dx/dt + x sin t = 1 is -

Assertion: Integrating factor of (dy )/(dx) + y = x^2 is e^x Reason: Integrating factor of ( dy )/(dx) + P( x) y= Q (x) is e^(int p(x) dx)

Assertion: Integrating factor of (dy )/(dx) + y = x^2 is e^x Reason: Integrating factor of ( dy )/(dx) + P( x) y= Q (x) is e^(int p(x) dx)