[" 3.Differentiale with reapect tha ze "],[qquad y=e^((x^(2)-3x+7))]

Differentiate the following with respect to x: (i) y=x^3 + 5x^2 + 3x+7 (ii) y=e^(x) + sin x+2 (iii) y=4 cosec x- "log" x-2e^(x)

In the following questions verify that the given function is a solution of the given differential equation : y = e^(x) + e^(2x) + e^(-3x), y''' - 7y' + 6y = 0

In the following questions verify that the given function is a solution of the given differential equation : y = e^(x) + e^(2x) + e^(-3x), y''' - 7y' + 6y = 0

y = e ^ (2x) + e ^ (3x)

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

The solution of the differential equation (dy)/(dx) = e^(3x-2y) +x^(2)e^(-2y) ,is

The general solution of the differential equation (d^2y)/dx^2=e^(-3x) is (A) y=9e^(-3x)+C_1x+C_2 (B) y=-3e^(-3x)+C_1x+C_2 (C) y=3e^(-3x)+C_1x+C_2 (D) y=e^(-3x)/9+C_1x+C_2

The general solution of the differential equation (d^2y)/dx^2=e^(-3x) is (A) y=9e^(-3x)+C_1x+C_2 (B) y=-3e^(-3x)+C_1x+C_2 (C) y=3e^(-3x)+C_1x+C_2 (D) y=e^(-3x)/9+C_1x+C_2

Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as Solution of the differential equation (dy)/(dx)=e^(3x-2y)+x^2e^(-2y) is (e^(2y))/(2)=(e^(3x))/(3)+(x^2)/(2)+C Reason (R) : (dy)/(dx)=e^(3x-2y)+x^2e^(-2y) (dy)/(dx)=e^(-2y)(e^(3x)+x^2) separating the variables e^(2y)dy=(e^(3x)+x^2)dx int e^(2y)dy=int(e^(3x)+x^2)dx (e^(2y))/(2)=(e^(3x))/(3)+(x^3)/(3)+C .

Solve : (dy)/(dx)=e^(3x-2y)+x^(2)e^(-2y)