I'll assume the ODE is
Solve the homogeneous ODE,
The characteristic equation
has roots at and
. Then the characteristic solution is
For nonhomogeneous ODE (1),
consider the ansatz particular solution
Substituting this into (1) gives
For the nonhomogeneous ODE (2),
take the ansatz
Substitute (2) into the ODE to get
Lastly, for the nonhomogeneous ODE (3)
take the ansatz
and solve for .
Then the general solution to the ODE is
Answer:
y = x
Step-by-step explanation:
slope-intercept form: y = mx + b
Given: slope(m) = , point (4, -3)
We already have the value of m, but we need to find the value of b. To do this, input the given values of the slope and the point into the equation:
-3 = (4) + b
Solve for b:
-3 = (4) + b
-3 = -3 + b
0 = b
The value of b is zero. We can now write the equation:
y = x + 0
y = x
The equation written in slope-intercept form is: y = x