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Match the following differential equation with its solution: 2x^2y" + 3xy' = y1. y =...

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bobby9901 | Student, College Freshman | (Level 1) Salutatorian

Posted September 3, 2012 at 7:10 PM via web

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Match the following differential equation with its solution:

2x^2y" + 3xy' = y

1. y = x^(1/2)

2. y = e^(-4x)

3. y = sin(x)

4. y = 3x + x^(2)

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lfryerda | High School Teacher | (Level 2) Educator

Posted September 3, 2012 at 8:26 PM (Answer #1)

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To match the differential equation with its answer, we need to take each of the functions, differentiate twice and combine to see if the left side of the differential equation matches with the right side.

(1)

`y=x^{1/2}`

` ` `y'=1/2x^{-1/2}`

`y''=-1/4x^{-3/2}`

`LS=-1/2x^{1/2}+3/2x^{1/2}=x^{1/2}=RS`

This is a solution.

(2)

`y=e^{-4x}`

`y'=-4e^{-4x}`

`y''=16e^{-4x}`

`LS=32x^2e^{-4x}-12xe^{-4x}=4x(8x-3)e^{-4x} ne RS`

This is not a solution

(3)

`y=sin x`

`y'=cos x`

`y''=-sin x`

`LS=-2x^2 sinx+3x cos x ne RS`

This is not a solution

(4)

`y=3x+x^2`

`y'=3+2x`

`y''=2`

`LS=4x^2+9x+6x^2=10x^2+9x ne RS`

The function (1) is a solution to the differential equation.

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