If `x=acostheta,y=bsintheta,` then prove that `(d^3y)/(dx^3)=(3b)/(a^3)cos e c^4thetacotthetadot`

If x=acos^3theta,y=bsin^3theta, f i n d (d^3y)/(dx^3) at theta=0.

If x=acostheta,y=bsintheta" then "(x^(2))/(a^(2))+(y^(2))/(b^(2))=?

If y= A sin x+ B cos x , then prove that (d^(2)y)/(dx^(2))+y=0 .

If y= 5 cos x-3 sin x , prove that (d^(2)y)/(dx^(2))+y=0 .

If x=acostheta and y=bsintheta then b^(2)x^(2)+a^(2)y^(2)= …………. .

If A B C having vertices A(acostheta_1,asintheta_1),B(acostheta_2asintheta_2),a n dC(acostheta_3,asintheta_3) is equilateral, then prove that costheta_1+costheta_2+costheta_3=sintheta_1+sintheta_2+sintheta_3=0.

If x = a cos^(3)(Theta), y = a sin^(3)(Theta) find (d^(2)y)/(dx^(2)) .

(a+bx)e^(y/x)=x , Prove that x^3(d^2y)/(dx^2)=(x(dy)/(dx)-y)^2

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