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The solution of the DE (dy)/(dx) = e ^...

The solution of the `DE (dy)/(dx) = e ^( x+ y )` is

A

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

B

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

C

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

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
The given DE is ` e ^(x)dx = e ^(-y) dy `.
`therefore int e ^(x) dx = int e ^(-y) dy rArr e ^(x) = - e^(-y) + C rArr e ^(x) + e ^(-y) = C `.
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RS AGGARWAL-LINEAR DIFFERENTIAL EQUATIONS -Objective Questions
  1. The solution of the DE (dy)/(dx) = e ^( x+ y ) is

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  2. The solution of the DE (dy)/(dx) = 2 ^( x + y ) is

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  3. The solution of the DE (e ^(x) + 1) y dy= ( y + 1) e ^(x) dx is

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  4. The solution of the DE x dy + y dx = 0 is

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  5. The solution of the DE x (dy)/(dx) = cot y is

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  6. The solution of the DE (dy)/(dx) = (( 1+y ^(2)))/((1 + x ^(2))) i...

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  7. The solution of the DE (dy)/(dx) = 1 - x + y - xy is

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  8. The solution of the DE (dy)/(dx) = e ^( x + y ) + x ^(2)* e ^(y...

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  9. The solution of the DE (dy )/(dx) + sqrt ((1 -y ^(2))/( 1- x ^(2))...

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  10. The solution of the DE (dy)/(dx) = (1 - cos x )/( 1+ cos x ) is

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  11. The solution of the DE (dy)/(dx) = (- 2 xy )/( ( x ^(2) + 1)) is

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  12. The solution of the DE cos x (1 + cosy )dx - sin y (1+ sin x ) dy=0 ...

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  13. The solution of the DE x cos y dy = (x e ^(x) log x + e ^(x)) dx is

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  14. The solution of the DE (dy)/(dx) + y log y cot x = 0 is

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  15. The general solution of the DE (1+ x ^(2)) dy - xy dx = 0 is

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  16. The solution of xsqrt(1+y^2)dx+ysqrt(1+x^2)dy=0

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  17. The solution of the equation log ((dy)/(dx))=a x+b y is (a) ( b ) (...

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  18. The general solution of the DE (dy)/(dx) = (sqrt (1 - x ^(2))) (sqrt...

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  19. The general solution of the DE (dy)/(dx) = ( y^(2)- x ^(2))/( 2xy ...

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  20. The general solution of the DE x ^(2) (dy)/(dx) = x ^(2) + xy + y ^...

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