Question

The Particular integral of the differential equation( D2+D+1)y=ex is equual to​

Answer 1

Answer:

We cannot eliminate a solution, thus we are left with two possibilities

y=ae(-'-1√2)x+Be(-1+√2)x+B

-32x

with a PI,

-47eax

Or, In standard form:

y '' +2y'-y=ea^x

Step-by-step explanation:

This is a second order linear non-Homogeneous Differentiation Equation with constant coefficients. The standard approach is to find a solution,

y

c

of the homogeneous equation by looking at the Auxiliary Equation, which is the quadratic equation with the coefficients of the derivatives, and then finding an independent particular solution,

y

p

of the non-homogeneous equation.