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If inta^x ty(t)dt=x^2+y(x), then find...

If `int_a^x ty(t)dt=x^2+y(x),` then find `y(x)`

A

` Y =2 -(2+a^2)e^(x^2-a^2/2)`

B

` Y =1 -(2+a^2)e^(x^2-a^2/2)`

C

` Y =2 -(1+a^2)e^(x^2-a^2/2)`

D

none

Text Solution

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The correct Answer is:
A
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MOTION-DIFFERENTIAL EQUATION -Exercise 2
  1. A curve passing through (2,3) and satisfying the differential equat...

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  2. Solve: x^2dy-y^2dx+xy^2(x-y)dy=0

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  3. If inta^x ty(t)dt=x^2+y(x), then find y(x)

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  4. If x(dy)/(dx)=y(log y -logx+1), then the solution of the equation is

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  5. Solution of the differential equation (x^(2)-y^(2))dx+2xy dy=0 is

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  6. The equation of the curve passing through origin and satisfying the di...

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  7. passes through a curve point (1,pi/4) and at some point Its gradation ...

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  8. A function satisfying int0^1f(tx)dt=nf(x), where x>0 is

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

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

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  11. The solution of differential equation (1+y^(2))+(x-e^(tan^(-1)y))(dy...

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  12. The solution of the differential equation, e^x(x +1)dx + (ye^y -xe^x)d...

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  13. The solution of y^5x+y-x dy/dx=0 is

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  14. The solution of the differential equation x^2(dy)/(dx)cos1/x-ysin1/x=-...

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

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

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

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  18. Solution of the equation (1 - x^2) dy + xy dx = xy^2dx is

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  19. Solve the differential equation (y^2+x^2)dx=(x^2+xy)dy

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  20. Find the particular solution of (cos x – x sin x +y^2)dx + 2xy dy = 0 ...

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