Question

3. If a curve y = f(x) passes through the point (1, –1) and satisfies the differential equation, y(1 + xy) dx = x dy, then f(-1/2) is equal to​

Answer 1

Answer:

y(1+xy)dx=xdy

y/x(1+xy)= dy/dx

y=vx⇒dy/dx =v+xdv/dx

∴v(1+vx^2 )=v+xdv/dx

v^2x^2 =xdv/dx

v^2x=dv/dx

∫xdx=∫1/v^2dv

x^2/2=-1/v+c

x^2/2 = -x/y+c

Put (1,-1)

1^2/2=-x/y-1/2

we have to find f(−1/2)

substitute x=−1/2

= (-1/2)^2/2=-(-1/2)/y-1/2

1/8=1/2y-1/2

y= 4/5

Answer 2

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hope it helps u Akshat!