In the lienar differential equation of the form `dy/dx+ Py = Q, `

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 -

Express the following differential equation in the form f(x)dx+g(y)dy=0 . (dy)/(dx)=(1+y^(2))/(1+x^(2))

Differential equations of the type (dy)/(dx)=f(x)