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Find the real value of m for which the s...

Find the real value of `m` for which the substitution `y=u^m` will transform the differential equation `2x^4y(dy)/(dx)+y^4=4x^6` in to a homogeneous equation.

A

m=0

B

m=1

C

`m=3/2`

D

`m=2/3`

Text Solution

Verified by Experts

The correct Answer is:
c
` y = u^(m) rArr (dy)/(dx) = mu^(m-1) (du)/(dx)`
Hence, ` 2x^(4) * u^(m) * mu^(m-1) * (du)/(dx) +u^(4m) = 4x^(6)`
` (du)/(dx) = (4x^(6)-u^(4m))/(2mx^(4)u^(2m-1))`
` rArr 4m = 6 rArr = 3/2`
` rArr 4m = 6rArr m = 3/2 `
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DIFFERENTIAL EQUATION-PRACTICE EXERCISE (Exercise 2 )
  1. A solution of y=2x (dy/dx) + x^2(dy/dx)^4 is

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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