If `y=ae^(x)+be^(-3x)+c`, then the value of `((d^(3)y)/(dx^(3))+2(d^(2)y)/(dx^(2)))/((dy)/(dx))` is

Find the degree of the differential equation ((d^(3)y)/(dx^(3))) + 2 ((d^(2)y)/(dx^(2))) + (dy)/(dx) + y = 0 .

Find the order of the differential equation (d^(3)y)/(dx^(3)) + 2((d^(2)y)/(dx^(2)))^(2) + (dy)/(dx) + y = 0

If x=sin theta and y=cos^(3) then 2y(d^(2)y)/(dx^(2))+4((dy)/(dx))^(2) is

If y ^(2) =3 cos ^(2)x+ 2 sin ^(2)x, then the value of y ^(4) +y^(3) (d^(2)y)/(dx ^(2)) is

If y=x^(4) , find (d^(2)y)/(dx^(2))and(d^(3)y)/(dx^(3)) .

If y=log(1+cosx) , prove that (d^3y)/(dx^3)+(d^2y)/(dx^2)dot(dy)/(dx)=0 .

The degree of the potential equation ((d^(2)y)/(dx^(2)))^(2)+((dy)/(dx))^(2)=x sin ((dy)/(dx))"is

The order and degree of differential equation: ((d^(3)y)/(dx^(3)))^(2)-3(d^(2)y)/(dx^(2))+2((dy)/(dx))^(4)=y^(4)"are"

If y=sin(log_(e)x) , then x^(2)(d^(2)y)/(dx^(2))+x(dy)/(dx) is equal to

Find the order and degree of the following differential equations. i) (dy)/(dx)+y=1/((dy)/(dx)) , ii) e^(e^(3)y)/(dx^(3))-x(d^(2)y)/(dx^(2))+y=0 , iii) sin^(-1)(dy)/(dx)=x+y , iv) log_(e)(dy)/(dx)=ax+by v) y(d^(2)y)/(dx^(2))+x((dy)/(dx))^(2)-4y(dy)/(dx)=0