" 8."y=sqrt(a^(2)-x^(2)),x in(-a,a):x+y(dy)/(dx)=0

y = sqrt(a^(2) - x^(2)) x ne (-a, a) : x + y (dy)/(dx) = 0(y ne 0)

y = sqrt(a^(2) - x^(2)) x ne (-a, a) : x + y (dy)/(dx) = 0(y ne 0)

y = sqrt(a^(2) - x^(2)) x ne (-a, a) : x + y (dy)/(dx) = 0(y ne 0)

y = sqrt(a^(2) - x^(2)) x ne (-a, a) : x + y (dy)/(dx) = 0(y ne 0)

sqrt(1+x^(2)+y^(2)+x^(2)y^(2))+xy(dy)/(dx)=0

if y=sqrt(x^(2)+a^(2)), then show that y(dy)/(dx)=x

If xy=a[y+sqrt(y^(2)-x^(2))] , prove that, x^(3)(dy)/(dx)=y^(2)(y+sqrt(y^(2)-x^(2)))

For each of the following differential equations verify that the accompanying functions a solution. Differential Function (a) x(dy)/(dx)=y, y=a x (b) x+y(dy)/(dx)=0, y=+-sqrt(a^2-x^2) (c) x(dy)/(dx)y=y^2, y=a/(x+a) (d) x^3(d^2y)/(dx^2)=1, y=a x+b+1/(2x) (e) y=((dy)/(dx))^2, y=1/4(x+-a)^2

For each of the following differential equations verify that the accompanying functions a solution. (i) x(dy)/(dx)=y => y=a x (ii) x+y(dy)/(dx)=0 => y=+-sqrt(a^2-x^2) (iii) x(dy)/(dx)y+y^2 => y=a/(x+a) (iv) x^3(d^2y)/(dx^2)=1 => y=a x+b+1/(2x) (v) y=((dy)/(dx))^2 => y=1/4(x+-a)^2

Solve the following differential equations. (i) (dy)/(dx) =(1+y^(2))/(1+x^(2)) (ii) (dy)/(dx) = (sqrt(1-y^(2)))/(sqrt(1-x^(2))) (iii) (dy)/(dx) = 2y tan hx (iv) sqrt(1+x^(2))dx + sqrt(1+y^(2))dy = 0 (v) (dy)/(dy) = e^(x-y)+x^(2)e^(-y)