Fill in the blanks `d/(dx) (2x + 3)` = ..................

Fill in the blanks d/(dx) (5x^2 - 7x +1) =..............

Given that d/(dx) (c_1u_1 +- c_2u_2 +- .........+- c_nu_n) = c_1d/(dx)(u_1) +- c_2d/(dx)(u_2) +- ....... +- c_nd/(dx)(u_n) and d/(dx) (c) = 0 if c,c_1,c_2,...........,c_n are constants and u_1, u_2,.....,u_n are functions of x. Using the given results, evaluate d/(dx) ((3x^2 + 12x - 11)/x)

Given that d/(dx) (c_1u_1 +- c_2u_2 +- .........+- c_nu_n) = c_1d/(dx)(u_1) +- c_2d/(dx)(u_2) +- ....... +- c_nd/(dx)(u_n) and d/(dx) (c) = 0 if c,c_1,c_2,...........,c_n are constants and u_1, u_2,.....,u_n are functions of x. After expanding the square, differentiate (sqrtx + 1/sqrtx)^2 w.r.t. x

The solution of the differential equation (dy)/(dx) = (3e^(2x) + 3e^(4x) )/( e^(x) + e^(-x) ) is a) y= e^(3x) + C b) y=2e^(2x) + C c) y= e^(x) + C d) y= e^(4x) + C

For each of the following differential equations, find a particular solution satisfying the given conditions. (dy)/(dx) - 3y cot x = sin 2x , y = 2 when x = pi/2

The degree of the differential equation [ 1 + ((dy)/(dx)) ^(2) ] ^((3)/(2)) = l (d ^(2) y)/(dx ^(2)) is

The solution of the differential equation log x (dy)/(dx) + (y)/(x) = sin 2x is a) y log | x | = C - (1)/(2) cos x b) y log |x| = C + (1)/(2) cos 2x c) y log | x| = C - (1)/(2) cos 2x d) xy log | x | = C - (1)/(2) cos 2x

Solve the following differential equations (dy)/(dx) + 3y = e^(-2x)