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avatarЛидия
Математика
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Solve y''+3y'+2y=e^-2x using D operator

10 июля 2017 г. 3:1714 Комментировать Следить
Ответы на вопрос | 1
avatarИрина
y′′−3y′+2y=x2 up vote 3 down vote favorite Solve y′′−3y′+2y=x2

My approach:

Homogen solution:

y=Aex+Be2x

Particular solution:

yp=x(Ax2+Bx+C)=Ax3+Bx2+Cx y′p=3Ax2+2Bx+C y′′p=6Ax+2B

Put his into the initial equartion to get A, B and C gives me: A=0,B=1/2,C=3/2

This leads me to the answer:

y=Aex+Be2x+x2/2+3x/2

However the correct answer is

y=Aex+Be2x+x2/2+3x/2+7/4

Where's my miss? Where comes the last term from?


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