a 14. ufay - AeMx + Beny, a fear fan dy -(m + n) + may = 0 dx dz2 + Relix

If y = Ae^(mx) + Be^(nx) , Show that (d^2 /dx^2 y)-(m+n)dy/dx+mny = 0

If x^m . Y^n = (x + y)^(m + n) , then dx/dy is :

If y= Ae^(mx) + Be^(nx) , show that (d^(2)y)/(dx^(2))- (m + n) (dy)/(dx) + mny= 0

If y = n^x, n > 0 then dy/dx is equal to

Let z_1a n dz_2 b be toots of the equation z^2+p z+q=0, where he coefficients pa n dq may be complex numbers. Let Aa n dB represent z_1a n dz_2 in the complex plane, respectively. If /_A O B=theta!=0a n dO A=O B ,w h e r eO is the origin, prove that p^2=4q"cos"^2(theta//2)dot

Let z_1a n dz_2 b be toots of the equation z^2+p z+q=0, where he coefficients pa n dq may be complex numbers. Let Aa n dB represent z_1a n dz_2 in the complex plane, respectively. If /_A O B=theta!=0a n dO A=O B ,w h e r eO is the origin, prove that p^2=4q"cos"^2(theta//2)dot