root(2 3)(" If "y=e^(4cos^(-1)x),-1<=x<=1," show that "(1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)-a^(2)y=0)

The number of roots of the equation sqrt(2)+e^(cos h^(-1) x)-e^(sin h^(-1) x)=0 is

The domain of the function f(x)=root(3)(1-3x)+3cos ^(-1)((2x-1)/(3)) is

If (dy)/(dx)+3/(cos^(2)x)y=1/(cos^(2)x),xin((-pi)/3,(pi)/3), and y((pi)/4)=4/3 , then y(-(pi)/4) equals 1/3+e^(k) . The value of k is __________.

If (dy)/(dx)+3/(cos^(2)x)y=1/(cos^(2)x),xin((-pi)/3,(pi)/3), and y((pi)/4)=4/3 , then y(-(pi)/4) equals 1/3+e^(k) . The value of k is __________.

If y=e^("sin"^(-1)x)andz=e^(-"cos"^(-1)x) , prove that dy/(dz)=e^(pi//2) .

The number of roots of equation ((x-1)(x-3))/((x-2)(x-4))-e^(x)) ((x+1)(x+3)e^x)/((x+2)(x+4))-1) (x^(3)-cos x)=0 :

If y = e^(m cos^(-1) x) (1-x^2)y_2-xy_1 = m^2y

Find number of real roots of equation e^(4x) + e^(3x) - 4e^(2x) + e^(x) + 1 = 0 is

Find number of real roots of equation e^(4x) + e^(3x) - 4e^(2x) + e^(x) + 1 = 0 is

If y=e^(tanx) , then (cos^2x)y2-(1+sin2x)y1=0