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1 Answer
- RapidfireLv 79 years agoFavorite Answer
This is not a separable differential equation so it cannot be solved that way.
Rewrite this differential equation in standard form:
dy / dx = 4x + y
dy / dx - y = 4x
Find the complementary function by solving the auxiliary equation:
dy / dx - y = 0
m - 1 = 0
m = 1
yᶜ = C℮˟
Find the particular integral by comparing coefficients:
yᵖ = Ax + B
dyᵖ / dx = A
dyᵖ / dx - yᵖ = 4x
A - (Ax + B) = 4x
A - Ax - B = 4x
(A - B) - Ax = 4x
-A = 4
A = -4
A - B = 0
B = A
B = -4
yᵖ = -4x - 4
Find the general solution by combining these two parts:
y = yᶜ + yᵖ
y = C℮˟ - 4x - 4
