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:
x = 20
Step-by-step explanation:
These angles are equal to each other because they are vertical angles.
Hence, we can equal the two measurements together to solve for x:
3x + 50 = 6x - 10
3x + 60 = 6x
60 = 3x
20 = x
Check your work:
3(20) + 50 = 6(20) - 10
60 + 50 = 120 - 10
110 = 110
Correct
Answer:
Step-by-step explanation:
Yes
Answer:
Step-by-step explanation:
x = 136/2 = 68°
Answer:
9x+9
Step-by-step explanation
Combine like terms (6x and 3x, 2 and 7)