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If x(t) is a solution of ((1+t)dy)/(d...

If `x(t)` is a solution of `((1+t)dy)/(dx)-t y=1` and `y(0)=-1` then `y(1)` is (a) `( b ) (c)-( d )1/( e )2( f ) (g) (h)` (i) (b) `( j ) (k) e+( l )1/( m )2( n ) (o) (p)` (q) (c) `( d ) (e) e-( f )1/( g )2( h ) (i) (j)` (k) (d) `( l ) (m) (n)1/( o )2( p ) (q) (r)` (s)

A

`-1/2`

B

`e+1/2`

C

`e-1/2`

D

`1/2`

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The correct Answer is:
A
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TARGET PUBLICATION-DIFFERENTIAL EQUATIONS -COMPETITIVE THINKING
  1. The solution of differential equation (1+y^(2))+(x-e^(tan^(-1)y))(dy...

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  2. The solution of (y-3x^2)dx +xdy=0 is

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  3. The solution of the equation (x-4y^3)"dy"/"dx"-y=0, (y gt 0) is

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  4. The solution of the differential equation y dx +(x +x^2 y) dy=0 is

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

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

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  7. The solution of the differential equation (xy^4 + y) dx-x dy = 0, is

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  8. The solution of (dy)/(dx) + y tan x = sec x is

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  9. The solution of the differential equation (dy)/(dx)+y/(x loge x)=1/x, ...

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  10. Let y(x) be the solution of the differential equation ( x log ...

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  11. Consider the differential equation y^2dx+(x-1/y)dy=0 if y(1)=1 then x ...

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  12. Let y(x) be a solution of (1+x^2)"dy"/"dx"+2xy-4x^2=0 and y(0)=-1 Th...

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  13. If x(t) is a solution of ((1+t)dy)/(dx)-t y=1 and y(0)=-1 then y(1)...

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  14. Solve the differential equation "dy=cos x(2-y cosec x)dx" given that y...

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  15. Let y^(prime)(x)+y(x)g^(prime)(x)=g(x)g^(prime)(x),y(0),x in R , wher...

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  16. Let y=g(x) be the solution of the differential equation sin (dy)/(dx...

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  17. If y(x) satisfies the differential equation y^(prime)-ytanx=2xs e c...

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  18. The population of a city increases at the rate 3% per year. If at time...

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  19. Let I be the purchase value of an equipment and V(t) be the value afte...

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  20. Let the population of rabbits surviving at a time t be governed by ...

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