Question

. 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:

(1) 4/5

(2) -2/5

(3) -4/5

(4) 2/5

Give reson.......
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Answer 1

Answer:

given equation of curves are

y² = >2x

which is a parabola with vertex (0,0) and parallel to x - axis

so it should e 4/5

Answer 2

Explanation:

QUESTION :-

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 :-

OPTION (A) IS CORRECT

DETAILED SOLUTION :-

y(1+xy)dx=xdy

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

y=vx⇒ dy/dx =v+x dv/ dx

∴ v(1+vx ^2 )= v+x dv/ dx

v ^2 x ^2 =x dv /dx

v ^2 x= dv/ dx

∫xdx=∫ 1 / v^2 dv

x ^2 / 2 = −1/ v +c

x ^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

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

y = 4/5

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@TheStellar♥️