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8 The solution of differential equation ...

8 The solution of differential equation `(dy)/(dx)=y/x+(phi(y/x))/(phi'(y/x))` is

A

`phi(y/x)=kx`

B

` x phi (y/x) = k`

C

` phi (y/x) = ky`

D

` y phi (y/x) = k`

Text Solution

Verified by Experts

The correct Answer is:
a
Given equation is , ` (dy)/(dx) = y/x + (phi(y/x))/(phi(y/x)`
Put ` y = vx rArr (dy)/(dx) = v+x (dv)/(dx)`
Now, Eq. (i) becomes
` v + x (dv)/(dx) = v+ (phi(v))/(phi'(v))`
` rArr (phi'(v))/(phi(v))dv = (dx)/x`
On integrating both sides, we get
` int (phi(v))/(phi(v)) dv = log x + log k`
` rArr log phi (v) = log xk`
` rArr phi (v) = kx rArr phi (y/x) = kx " " [ :' v = y/x]`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DIFFERENTIAL EQUATION-PRACTICE EXERCISE (Exercise 2 )
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  2. The differential equation y(dy)/(dx) + x = c represents

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  3. 8 The solution of differential equation (dy)/(dx)=y/x+(phi(y/x))/(phi'...

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  4. The general solution of (dy)/(dx) = 2x e^(x^(2)-y) is

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  5. The solution of the differential equation (dy)/(dx) = (x(2 log x...

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  6. A solution of y=2x (dy/dx) + x^2(dy/dx)^4 is

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  7. The solution of differential equation (dy)/(dx) + xy = xy^(2) is

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  8. Find the real value of m for which the substitution y=u^m will transfo...

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  9. The solution of differential equation (dy)/(dx) = e^(x-y) + x^(2)e^(-y...

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  10. If x^2+y^2=1 then (y'=dy/dx, y''=(d^2y)/dx^2)

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  11. (dy)/(dx)+(3x^2)/(1+x^3)y=(sin^2x)/(1+x^3)

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  12. Solution of the differential equation (dy)/(dx)+ytanx=x^(n)cosx is

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  13. The solution of differential equation (xy^(5)+2y)dx-xdy =0, is

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  14. The solution of the differential equation dy/dx=sin(x+y)+cos(x+y) is:

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  15. The solution of the differential equation x^(4)(dy)/(dx)+x^(3)y+"cosec...

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  16. If the solution of the differential equation (dy)/(dx)=(ax+3)/(2y+f)...

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

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

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

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

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