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The solution of the differential equatio...

The solution of the differential equation `(dy)/(dx)+1=e^(x+y),` is a. `(x+y)e^(x+y)=0` b. `(x+C)e^(x+y)=0` c. `(x-C)e^(x+y)=1` d. `(x+C)e^(x+y)+1=0`

A

`(x+y)e^(x+y)=0`

B

`(x+C)e^(x+y)=0`

C

`(x-C)e^(x+y)=1`

D

`(x+C)e^(x+y)+1=0`

Text Solution

Verified by Experts

The correct Answer is:
D
We have,
`(dy)/(dx)+1=e^(x+y)`
Let `x+y=v`. Then, `1+(dy)/(dx)=(dv)/(dx)`
`therefore" "(dy)/(dx)+1=e^(x+y)`
`rArr" "(dv)/(dx)=e^(v)`
`rArr" "e^(-v)dv=dx`
`rArr" "inte^(-v)dv=intdx`
`rArr" "-e^(-v)=x+C`
`rArr" "-e^(-(x+y))=x+C rArr (x+C) e^(x+y)+1=0`
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OBJECTIVE RD SHARMA ENGLISH-DIFFERENTIAL EQUATIONS-Chapter Test
  1. The solution of the differential equation (dy)/(dx)+1=e^(x+y), is a. (...

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  2. (x^(2)+y ^(2)) dy = xydx. If y (x (o)) =e, y (1)=1, then the value of ...

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  3. The differential equation of the family of curves y^(2)=4xa(x+1), is

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  4. y=ae^(mx)+be^(-mx) satisfies which of the following differential equat...

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  5. The solution of the differential equation (dy)/(dx)=e^(y+x)+e^(y-x), i...

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  6. The differential equation of the family of curves y=e^(2x)(a cos x+b s...

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  7. The differential equation obtained on eliminating A and B from y=A c...

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  8. The solution of (dy)/(dx)=((y)/(x))^(1//3), is

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  9. The slope of the tangent at (x , y) to a curve passing through a po...

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  10. Solve Y-X(dy)/(dx)=a(y^(2)+(dy)/(dx))

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

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

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  13. The solution of (dy)/(dx)-y=1, y(0)=1 is given by

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  14. The number of solution of y'=(x+1)/(x-1),y(1)=2, is

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  15. What is the solution of y'=1+x+y^(2)+xy^(2),y(0)=0?

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  16. Solution of the differential equation x(dy)/(dx)=y+sqrt(x^(2)+y^(2)), ...

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  17. Integral curve satisfying Y'=(x^2 +y^2)/(x^2-y^2) y' (1) ne 1 has th...

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  18. The differential equation which represents the family of plane curves ...

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  19. A continuously differentiable function y=f(x) , x in ((-pi)/(2) ,(pi)/...

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  20. The solution of the differential equation (d^(2)y)/(dx^(2))=e^(-2x), i...

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  21. The order and degree of the differential equation (d^(2)y)/(dx^(2))=sq...

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