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The solution of the differential equatio...

The solution of the differential equation
`ye^(x//y)dx=(xe^(x//y)+y^(2)siny)dy` is

A

`e^(x//y)=x+C`

B

`e^(x//y)+x=C`

C

`e^(y//x)=x+C`

D

`e^(x//y)=y+C`

Text Solution

Verified by Experts

The correct Answer is:
d
Given , differential eqution is ` ye^(x//y) dx= (xe^(x//y) + y^(2))dy `
` rArr e^(x//y) (dx)/(dy) = x/y e^(x//y)+y`
` rArr e^(x//y) (dx)/(dy) - x/ye^(x//y)=y " "` …(i)
Then Eq, (i) becomes ,
` e^(v) (v+y(dy)/(dx))-ve^(v) = y rArr e^(v)y (dv)/(dy) = y `
` rArr e^(v) (dv)/(dx) = 1 rArr e^(v) dv = dy`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DIFFERENTIAL EQUATION-PRACTICE EXERCISE (Exercise 2 )
  1. The solution of the differential equation xy(dy)/(dx)={(1+y^2)(1+x+x^2...

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  2. Find the equation of the curve such that the portion of the x-axis ...

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  3. The solution of the differential equation ye^(x//y)dx=(xe^(x//y)+y^(...

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  4. The solution of the differential equation x (dy)/(dx) - y + x sin ...

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  5. The solution of the differential equation x dx + y dy+ (x dy - y d...

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  6. Observe the following statement . I . If dy + 2xy dx = 2e^(-x^(2))...

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  7. The solution of x (dy)/(dx) = y+2 sqrt(y^(2)-x^(2)) is

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  8. Solution of x (dy)/(dx) + y = x^(2) y^(4) is

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  9. The solution of differential equation (dt)/(dx) = (t[d/dx{g(x)}]-...

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  10. The differential equation y(dy)/(dx) + x = c represents

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  11. 8 The solution of differential equation (dy)/(dx)=y/x+(phi(y/x))/(phi'...

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

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

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

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

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

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

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

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

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

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