Solving Second Order Linear Differential Equation by Using D-operator
Not what you're looking for? Search our solutions OR ask your own Custom question.
Use D-operators to find a particular solution to the differential equation:
y^n + y' - 2y= e^-2x
Hence write its general solution. Find the solution that satisfies the initial conditions:
y(0) = 1/3, y'(0) = -1/3
https://brainmass.com/math/ordinary-differential-equations/solving-second-order-linear-differential-equation-d-operator-576598
SOLUTION This solution is FREE courtesy of BrainMass!
Solution:
The characteristic equation is
so the complementary solution will be
Given
Let f(D) =
Since f(-2) = 0
f'(D) = 2D+1
f'(-2) = 2(-2)+1 = -3
So particular integral will be
so the general solution will be
Given y(0) = 1/3
Now,
Given y'(0) = -1/3
Subtract equation (ii) from equation (i)
3c1 = 1/3
c1 = 1/9
Thus, general solution will be
Answer:
© BrainMass Inc. brainmass.com December 24, 2021, 11:31 pm ad1c9bdddf>https://brainmass.com/math/ordinary-differential-equations/solving-second-order-linear-differential-equation-d-operator-576598