solve (D²+4D+4)y=e-²x
Answers
Answer:
What is the particular integral of (D^2+D+4) y=e^2x? Is D = dy/dx, or is it a constant.
To answer your second question (D2+D+4)y=d2ydx2+dydx+y . The D is an operator which means to find the derivative of its operand with respect to x in this case.
The way to find the particular integral or particular solution is to make an educated guess on the form of it with constant coefficients and check if it's correct. If it's correct, then you solve for the coefficients. If it's not correct, then it will be impossible to solve for the coefficients.
Let's guess that yp=Ae2x .
y′p=2Ae2x
y′′p=4Ae2x
(D2+D+4)yp=(4A+2A+4A)e2x=10Ae2x=e2x
A=110
The particular integral is yp=110e2x .
Step-by-step explanation:
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