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`

Verify that the given function is a solution of the differential equation: y_1+y=0, y=ce^-x

In the following questions verify that the given function is a solution of the given differential equation : y = a cos (wx + y) , y y''' - y.y'' = 0

In the following question verify that the given function is a solution of the given differential equation : y = a cos (wx + y) , y y''' - y.y'' = 0

In the following questions verify that the given function is a solution of the given differential equation : y = c_(1) sin x + c_(2)cos x , (d^(2)y)/(d x^(2)) +y =0

In the following questions verify that the given function is a solution of the given differential equation : y = c_(1) sin x + c_(2)cos x , (d^(2)y)/(d x^(2)) +y =0

verify that the given function is a solution of the differential equations : y''+y=0, y = A cos x - B sin x .

verify that the given function is a solution of the differential equations : y''+4y=0, y = A cos 2x-B sin 2x .

Verify that the given function is a solution of the differential equation: y_3-6=0, y=x^3+ax^2+bx+c .

Verify that the given function is a solution of the differential equation: (y-x)dy-(y^2-x^2)dx=0 , y=-x-1 .

Verify that the given function is a solution of the differential equation: y_2+4y=0 , y=Acos2x+Bsin2x