Write the given Differential Equation in the form Ly gx whe

Solution

given equation can be written as:

2y\" -3y\' -2y = 1

or

y\" -1.5y\' -y = 0.5

this differential is solved by finding complementry solution and particular solution

complementry solution:

it can be find by solving, m² -1.5m -1 = 0

which gives m = 2, -0.5

so we have: Ae^2x +Be^-0.5x

now particular solution:

we have y = 1/(m² -1.5m -1 )

it can be written as: e^0x/(m² -1.5m -1)

as coefficient of t in power of t is 0 so put m = 0

we get y = -1

so overall solution

y = complementry solution + particular solution = Ae^2x + Be^-0.5x -1

ie y = Ae^2x + Be^-0.5x -1