If y\'\' + 4y\' = 2x, then, with C 1 and C 2 arbitrary, y = Question 8 options:

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If y'' + 4y' = 2x, then, with C1 and C2 arbitrary, y = Question 8 options: A) x2 - x/2 + C1e-4x + C2 B) x2/2 - x/4 + C1e-4x + C2 C) x2/4 - x/8 + C1e-8x + C2 D) 2x2 - 2x + C1e-2x + C2 E) x2 - x + C1e-2x + C2 F) x2/4 - x/8 + C1e-4x + C2 G) x2/2 - x/8 + C1e-8x + C2 H) x2/2 - x/2 + C1e-2x + C2 I) x2/8 - x/32 + C1e-8x + C2 J) none of these If y'' + 4y' = 2x, then, with C1 and C2 arbitrary, y = If y'' + 4y' = 2x, then, with C1 and C2 arbitrary, y = A) x2 - x/2 + C1e-4x + C2 B) x2/2 - x/4 + C1e-4x + C2 C) x2/4 - x/8 + C1e-8x + C2 D) 2x2 - 2x + C1e-2x + C2 E) x2 - x + C1e-2x + C2 F) x2/4 - x/8 + C1e-4x + C2 G) x2/2 - x/8 + C1e-8x + C2 H) x2/2 - x/2 + C1e-2x + C2 I) x2/8 - x/32 + C1e-8x + C2 J) none of these A) x2 - x/2 + C1e-4x + C2 B) x2/2 - x/4 + C1e-4x + C2 C) x2/4 - x/8 + C1e-8x + C2 D) 2x2 - 2x + C1e-2x + C2 E) x2 - x + C1e-2x + C2 F) x2/4 - x/8 + C1e-4x + C2 G) x2/2 - x/8 + C1e-8x + C2 H) x2/2 - x/2 + C1e-2x + C2 I) x2/8 - x/32 + C1e-8x + C2 J) none of these A) x2 - x/2 + C1e-4x + C2 B) x2/2 - x/4 + C1e-4x + C2 C) x2/4 - x/8 + C1e-8x + C2 D) 2x2 - 2x + C1e-2x + C2 E) x2 - x + C1e-2x + C2 F) x2/4 - x/8 + C1e-4x + C2 G) x2/2 - x/8 + C1e-8x + C2 H) x2/2 - x/2 + C1e-2x + C2 I) x2/8 - x/32 + C1e-8x + C2 J) none of these

Explanation / Answer

Characteristic equation: r^2 + 4r = 0

--> r(r+4) = 0 --> roots are 0 , -4

The homogeneous solution is: yh = C1 e-4t + C2

The particular solution is:

y = Ax2 + Bx

--> y' = 2Ax + B

--> y" = 2A

--> y" + 4y' = 8Ax + 4B + 2A = 8x

--> A = 1 , B = -1/2

So the final solution is:

y = C1 e-4x + C2 + x2 - 1/2 x

so answer is A) x2 - x/2 + C1e-4x + C2

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