`y=e^(ax)cosbx` then find `y_n(0)`.

int(e^(ax).cosbx)dx

If y = y(x) and it follows the relation e^(xy) + y cos x = 2 , then find (i) y'(0) and (ii) y"(0) .

Suppose y=e^(a x)+e^(b x) , find y''

If y=e^(ax) sin bx then prove that (d^2y)/(dx^(2))-2a(dy)/(dx)+(a^(2)+b^(2))y=0 .

If y=e^(-x) cos x and y_n+k_ny=0 where yn=(d^ny)/(dx^n) and k_n are constant n in N then

If y=e^(-x) cos x and y_n+k_ny=0 where yn=(d^ny)/(dx^n) and k_n are constant n in N then

If y=(log)_e x , then find y when x=3 and x=0. 03 .

If the area of the triangle included between the axes and any tangent to the curve x^n y=a^n is constant, then find the value of ndot

If the area of the triangle included between the axes and any tangent to the curve x^n y=a^n is constant, then find the value of ndot

"If "log_(e)(log_(e) x-log_(e)y)=e^(x^(2_(y)))(1-log_(e)x)," then find the value of "y'(e).