" 1."x^(2)dy+y(x+y)dx=0

If y=sqrt((1-x)/(1+x)), find (dy)/(dx) and prove that (1-x^(2))(dy)/(dx)+y=0

Solve: x^(2)(x dx+y dy)+2y(x dy-y dx)=0

If y=sin^(-1)x then prove that (1-x^(2))(d^(y))/(dx^(2))-x(dy)/(dx)=0

lf y=sqrt((1-x)/(1+x)) find dy/dx and prove that (1-x^2)(dy)/(dx)+y=0

y dx+(x-y^2)dy=0

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

2 x y+y^2-2 x^2 (dy)/(dx)=0 , y=2 when x=1

Which of the following differential equations has y = x as one of its particular solution? (A) (d^2y)/(dx^2)-x^2(dy)/(dx)+x y=x (B) (d^2y)/(dx^2)+x(dy)/(dx)+x y=x (C) (d^2y)/(dx^2)-x^2(dy)/(dx)+x y=0 (D) (d^2y)/(dx^2)+x(dy)/(dx)+x y=0

The solution of (x dx+y dy)/(x dy-y dx)=sqrt((1-x^2-y^2)/(x^2+y^2)) is

Solve the differential equation: (i) (1+y^(2))+(x-e^( tan ^(-1)y))(dy)/(dx)=0 (ii) x(dy)/(dx)+cos^(2)y=tan y(dy)/(dx)