If `y=x+x^(2)/2+x^(3)/3+x^(4)/4+...` then show that `x=y-y^(2)/(2!)+y^(3)/(3!)-y^(4)/(4!)+...`

3x-2y=(5)/(2),(1)/(3)x+3y=(-4)/(3)

If (x+iy)^(3)= u +iv , then show that (u)/(x)+(v)/(y)=4(x^(2)-y^(2)) .

Find the slope at x=2 for y=x^(4)-4x^(3)

If y= 3 cos (log x)+4 sin(log x) , show that x^(2)y_(2)+xy_(1)+y=0 .

(1)/(3)x+y=(10)/(3),2x+(1)/(4)y=(11)/(4)

(1)/(2(3x+4y))=(1)/(5(2x-3y))=(1)/(4),

If the points (x_1, y_1),(x_2,y_2), and (x_3, y_3) are collinear show that (y_2-y_3)/(x_2x_3)+(y_3-y_1)/(x_3x_1)+(y_1-y_2)/(x_1x_2)=0

Find x and y if x((4), (-3))x+y((-2), (3))=((4), (6)) .