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y``+y`+9.25y=2+2x+x^2

my problem:

yh=c1+c2e^(-x)

suppose yp=c3x^2 + c4x+c5

then yp`=2c3x+c4

so yp``=2c3

then 2c3+2c3x+c4=2+2X+X^2

so c3=1, c4=1

so yp=x^2+x

then y=c1+c2e^(-x)+x^2+x

which implies c1=8

=> y=8+c2e^(-x)+x^2+x

so y`=-c2e^(-x)+2x+1

so -1=-c2+1 =>c2=2

then y=8+2e^(-x)+x^2 +x

but the correct answer should be 3e^(-x)+5+2x+(1/3)x^3

does anybody know what's wrong with the calculations?

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# Homework Help: One more 2nd order D.E.

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