Let yprime(x)+y(x)gprime(x)=g(x)gprime(x),y(0)=0,x∈R, where fprime(x) denotes dxdy(x), and g(x) is a given non-constant differentiable function on R with g(0)=g(2)=0. Then the value of y(2) is______
A homogeneous differential equation of the from dydx=h(yx)can be solved by making the substitution.(A) y=vx (B) v=yx (C) x=vy (D) x=v
In a bank, principal increases continuously at the rate of 5% per year. In how many years Rs 1000 double itself?
Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.y=ae3x+be−2x
At any point (x, y) of a curve, the slope of the tangent is twice the slope of the line segment joining the point of contact to the point (4,3). Find the equation of the curve given that it passes through (2,1).
Verify that the given function (implicit or explicit) is a solution of the corresponding differential equation.(i) y=aex+be−x+x2 : xdx2d2y+2ydxdy−xy+x2−2=0
Form the differential equation representing the family of curves given by (x−a)2+2y2=a2, where a is an arbitrary constant.