What is the integrating factor of the differential equation (1−y2)dydx+xy=ay(−1<y<1)
Let f be a real-valued differentiable function on R (the set of all real numbers) such that f(1)=1. If the y−∈tercept of the tangent at any point P(x,y) on the curve y=f(x) is equal to the cube of the abscissa of P, then the value of f(−3) is equal to________
Consider the equation a2+λx2+b2+λy2=1, where a and b are specified constants and λ is an arbitrary parameter. Find a differential equation satisfied by it.
The order and degree of the differential equation of parabolas having vertex at the origin and focus at (a, 0) where a > 0, are respectively
The population of a country doubles in 40 years. Assuming that the rate of increase is proportional to the number of inhabitants, the number of years in which it would treble itself is