# Match each of the following differential equation with its solution: xy'-y = x^2 1. y = x^(1/2) 2. y = e^(-4x) 3. y = sin(x) 4. y = 3x + x^(2)

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Expert Answers

jeew-m | Certified Educator

`y = x^(1/2)`

`y' = 1/(2sqrtx)`

`xy'-y`

`= x*1/(2sqrtx)-x^(1/2)`

`= [x-2(sqrtx)^2]/(2sqrtx)`

`= -x/(2sqrtx)`

`= -sqrtx/2`

`y = e^(-4x)`

`y' = -4e^(-4x)`

`xy'-y`

`= x(-4e^(-4x))-e^(-4x)`

`= e^(-4x)(-4x-1)`

`= -e^(-4x)(4x+1)`

`y = sin(x)`

`y' = cosx`

`xy'-y`

`= xcosx-sinx`

`y = 3x + x^(2)`

`y' = 3+2x`

`xy'-y`

`= x(3+2x)-(3x + x^(2))`

`= 3x+2x^2-3x-x^2`

`= x^2`

**So the answer is `y = 3x + x^(2)` or the answer is (4)**