Determine a homogeneous linear differential equation with co

Determine a homogeneous linear differential equation with constant coefficients having as two of its solutions: 3sin(5x) and 2x^2-1. Use differential operator notation and you may leave it in factored form.

The differential equation having 3sin(5x) as solution is

y\'\'+25y=0

In operator form

(D^2+25)y=0

D=d/dx

Now note that 2x^2-1 is quadratic so under a third derivative it will vanish

So,

D^3(D^2+25)y=0 will have a quadratic as a solution

So required ode is

(D^5+25D^3)y=0

y\'\'\'\'\'+25y\'\'\'=0

Determine a homogeneous linear differential equation with constant coefficients having as two of its solutions: 3sin(5x) and 2x^2-1. Use differential operator

Determine a homogeneous linear differential equation with co

Solution

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