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Solve: (dy)/(dx) = (yf^(')(x)-y^(2))/(...

Solve:
`(dy)/(dx) = (yf^(')(x)-y^(2))/(f(x))`

A

`f(x)=y+C`

B

`f(x)=y(x+C)`

C

`f(x)=x+C`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
b
The given equation is
` (dy)/(dx) = (yf'(x)-y^(2))/(f(x))`
` rArr yf'(x)dx -f (x) dy = y^(2) dx`
` rArr (yf'(x)dx - f(x)dy)/(y^(2)) = dx rArr d[(f(x))/y ] =dx`
On integration ,we get
` (f(x))/y = x+C rArr f(x) = y (x+C)`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DIFFERENTIAL EQUATION-PRACTICE EXERCISE (Exercise 2 )
  1. If the solution of the differential equation (dy)/(dx)=(ax+3)/(2y+f)...

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  2. If xdy = y(dx + ydy); y(1) = 1 and y(x) > 0, then what is y(-3) equal ...

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  3. Solve: (dy)/(dx) = (yf^(')(x)-y^(2))/(f(x))

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  4. The solution of the differential equation (dy)/(dx)=(a x+g)/(b y+f) re...

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  5. The solution of the differential equation (dy)/(dx)=(a x+g)/(b y+f) re...

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  6. The solution of the differential of the differential equation (dy)/...

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  7. The solution of the differential equation (x+y)^(2)(dy)/(dx) = a^(2...

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  8. The solution of differential equation cos x dy = y (sin x - y ) dx,...

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  9. The equation of one of the curves whose slope of tangent at any point ...

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  10. The general solution of the differential equation (dy)/(dx)+(1+cos2y)/...

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  11. The solution of (dy)/(dx) = (ax + h)/(by + k) represents a parabola wh...

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  12. The solution of differential equation [ e^(-2sqrt(2))/(sqrt(x))-y/(...

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  13. The integrating factor of the differential equation (y log y) dx = (l...

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  14. The solution of the differential equation (dy)/(dx) = 1/(x+y^(2)) is

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  15. Integrating factor of the differential equation (x.logx)(dy)/(dx)+y=2l...

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  16. Solution of the equation x^(2)y - x^(3)(dy)/(dx)=y^(4)cosx , when y(0)...

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  17. The solution of the differential equation (1+y^2)+(x-e^(tan^-1y))dy/dx...

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  18. The solution of the differential equation (dy)/(dx)=(x+y)/x satisfyi...

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  19. The integrating factor of the differential equation (dy)/(dx)+(y)/((1-...

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  20. The solution of the differential equation (dy)/(dx)-y tan x=e^(x)sec x...

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