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Find a particular solution to the

differential equation
−2y′′−1y′+1y=1t²−2t+2e⁻³ᵗ
yₚ =

1 Answer

4 votes

Final answer:

To find a particular solution to the given differential equation, we use the forms of the non-homogeneous terms (polynomial and exponential). By substituting these particular solutions into the equation and solving for the coefficients, we can find the particular solution.

Step-by-step explanation:

The given differential equation is -2y'' - y' + y = t² - 2t + 2e⁻³ᵗ

To find a particular solution to this equation, we need to consider the form of the non-homogeneous terms. In this case, it consists of a polynomial (t² - 2t) and an exponential term (2e⁻³ᵗ).

For the polynomial term, we can assume a particular solution of the form yp = At² + Bt + C. And for the exponential term, we can assume a particular solution of the form yp = De⁻³ᵗ.

Substituting these particular solutions into the differential equation and solving for the coefficients A, B, C, and D will give us the particular solution to the equation.

User Ray Doyle
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