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The solution of the differential equatio...

The solution of the differential equation ` x(dy)/(dx) = 2y + x^(3)e^(x),` where y = 0 when x = 1 is

A

`y = x^(2)(e^(x)-e)`

B

`y = x^(3) (e-e^(x))`

C

`y=x^(2) (e^(x)-e)`

D

` y = x^(2) (e-e^(x))`

Text Solution

Verified by Experts

The correct Answer is:
c
Given , `(dy)/(dx) - 2 /x y = x^(2)e^(x)`
` :. IF = e^(-int 2/x dx) = e^(-logx^(2)) = 1/(x^(2))`
Given y = 0 , when x = 1 then C = -e
` :. Y = x^(2) (e^(x)-e)`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DIFFERENTIAL EQUATION-PRACTICE EXERCISE (Exercise 2 )
  1. The solution of the differential equation (dy)/(dx)-y tan x=e^(x)sec x...

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  2. (1 + x^(2)) (dy)/(dx) + 2xy = 4x ^(2), given that y = 0, when x =0

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  3. The solution of the differential equation x(dy)/(dx) = 2y + x^(3)e^(x...

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  4. The solution of the differential equation (dy)/(dx) = y tan x - 2 si...

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  5. The family of curves y = e^(a sinx) where a is an arbitrary constant ...

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  6. The differential equation of the family y = ae^(x) + bx e^(x) + cx^(2)...

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  7. The order and degree of the differential equation of all tangent lin...

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  8. The general solution of y^(2)dx+(x^(2)-xy+y^(2))dy=0, is

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  9. The general solution of the differential equation (dx)/(dy)+(x/y)^2-...

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  10. The general solution of the differential equaiton (1+y^(2))dx+(1+x^(2)...

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  11. The solution of (dy)/(dx)+1 = e^(x+y) is

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  12. The differential equation (dy)/(dx) = (x(1+y^(2)))/(y(1+x^(2)) repres...

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  13. If xsin((y)/(x))dy=[ysin((y)/(x))-x]dx ad y(1)=(pi)/(2), then the valu...

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  14. Solution of the differential equation tan y.sec^(2) x dx + tan x. sec^...

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  15. The solution of e^(dy//dx) = (x+1) , y (0) = 3 is

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

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  17. If C is an arbitrary constant , then the general solution of the diffe...

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  18. Find the differential equation of system of cocentric circles with cen...

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  19. If a curve passes through the point (2,7/2) and has slope (1-1/(x^(2)...

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  20. The population p(t) at time t of a certain mouse species satisfies the...

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