The line y = mx +1 is a tangent to y² = 4x if m equals

The solution for L (t² e^2t) is

The number of real roots of the equation 

(x-1)²+(x-2)²+(x-3)² = 0 is 

Order & degree of differential equation d²y/dx²={y+[dy/dx]²}^1/4 are

Solution of differential equation xdy-ydx=0 represents

The auxiliary equation of (aD²+bD+c) = 0 is having two real & distinct roots m₁ & m_² then the general solution is