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The solution of (dy)/(dx)+y=e^(-x), y(0)...

The solution of `(dy)/(dx)+y=e^(-x), y(0)=0 "is"`

A

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

B

`y=xe^(x)`

C

`y=xe^(-x)+1`

D

`y=xe^(-x)`

Text Solution

Verified by Experts

The correct Answer is:
D
Given that, `" "(dy)/(dx)+y=e^(-x)`
which is a linear differential equation
Here, `P=1 and Q=e^(-x)`
`" "IF=e^(intdx)=e^(x)`
The general solution is
`" "y*e^(x)=inte^(-x)*e^(x)dx+C`
`rArr" "ye^(x)=intdx+C`
`rArr" "ye^(x)=x+C" "`...(i)
When x=0 and y=0 then, 0=0+C `rArr` C=0
Eq. (i) becomes `y*e^(x)=xrArr=xe^(-x)`
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NCERT EXEMPLAR-DIFFERENTIAL EQUATIONS -Differential Equations
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  2. The differential equation of the family of curves of x^(2)+y^(2)-2ay=0...

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  3. The family y=Ax+A^(3) of curves is represents by differential equation...

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  4. The general solution of (dy)/(dx)=2xe^(x^(2)-y) is

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  5. The curve for which the slope of the tangent at any point is equal to ...

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  6. The general solution of differential equation (dy)/(dx)=e^((x^(2))/(2)...

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  7. The solution of equation (2y-1)dx-(2x+3)dy=0 is

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  8. The differential equation for which y=a cos x+b sin x is a solution is

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  9. The solution of (dy)/(dx)+y=e^(-x), y(0)=0 "is"

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  10. The order and degree of differential equation: ((d^(3)y)/(dx^(3)))^(...

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  11. The order and degree of differential equation: [1+((dy)/(dx))^(2)]=(d^...

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  12. The differential equation of family of curves of y^(2)=4a(x+a)is

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  13. Which of the following is a general solution of (d^(2)y)/(dx^(2))-2(dy...

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

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  15. The solution of differential equation (dy)/(dx)+(y)/(x)=sin x is

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  16. The general solution of differential equation (dy)/(dx)=e^((x^(2))/(2)...

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  17. The solution of differential equation (dy)/(dx)=e^(x-y)+x^(2)e^(-y)is

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  18. The solution of differential equation (dy)/(dx)+(2xy)/(1+x^(2))=(1)/(1...

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  19. (i) The degree of the differential equation (d^(2)y)/(dx^(2))+e^(dy//d...

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  20. State True and False for the following (i) Integrating factor of the...

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