2 years ago
The table that is needed has been provided in the images.
Given the differential = y"" - 8y'+16y=-3e^(4x).
a) Find the complementary solution =y_(c) to the differential equation.
b) Write down the FORM of the particular solution =y_(p) for a solution using undetermined coefficients. DO NOT solve for =y_(p). Use Table. 4.4.1
= y_(p)=__________________________
2 Answers
Best Answer
brianwilsonticketsglasgow Staff answered 2 years ago
brianwilsonticketsglasgow Staff answered 2 years ago
Step 1
Given differential equation
=y""-8y'+16y=-3e^(4x).
The auxiliary equation covespoding to homogen equation is
=m^(2)-8m+16=0
Solve form
=(m-4)^(2)=0
= -> m=4,4
The multiplicity of the root m=4 is 2 which gives
=y_(1)(x)=c_(1)e^(4x) and = y_(2)(x)=c_(2)e^(4x)* x
Where =c_(1) and c_(2) are constant
The complementary solution is sum of the above solutions:
=y_(c)(x)=y_(1)(x)+y_(2)(x)
= -> y_(c)(x)=c_(1)e^(4x)+c_(2)e^(4x)* x
Best Answer
Daddyyes Staff answered 2 years ago
Daddyyes Staff answered 2 years ago
Step 2
Now.
Defermine the particular solution to y""-8'+16y=-3e^(4x). by the method of undertemined coefficietns:
The particular solution to
=y""-8'+16y=-3e^(4x) is of the form
=y_(p)(x)=x^(2)(a_(1)e^(4x)) where =a_(1) where a_(1)e^(4x) was multiplied by x^(2) to account for e^(4x)x in the complementary solution.