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Title: Reduction of Order for second order differential equations
Description: Reduction of order requires that a solution already be known. Without this known solution we wonβt be able to do reduction of order. Therefore, this file shows you the two cases of reduction methods ( homogeneous and non-homogeneous ODE) supported by three solved examples in details.
Description: Reduction of order requires that a solution already be known. Without this known solution we wonβt be able to do reduction of order. Therefore, this file shows you the two cases of reduction methods ( homogeneous and non-homogeneous ODE) supported by three solved examples in details.
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4
...
π¦ β²β² + π( π₯ ) π¦ β² + π ( π₯ ) π¦ = π(π₯)
The procedure:
1- If it is homogenous: π¦ β²β² + π( π₯ ) π¦ β² + π ( π₯ ) π¦ = 0
Use the formula directly: π¦2 = π¦1 β«
π β β« π(π₯)ππ₯
π¦12
ππ₯
2- if it is non-homogenous: π¦ β²β² + π( π₯ ) π¦ β² + π ( π₯ ) π¦ =
π(π₯)
Use the following:
1- π¦2 = π¦1 Γ π’
β²
2- π‘βπ π·
...
E you
get linear first order in w and x
4- Now solve by 2
Title: Reduction of Order for second order differential equations
Description: Reduction of order requires that a solution already be known. Without this known solution we wonβt be able to do reduction of order. Therefore, this file shows you the two cases of reduction methods ( homogeneous and non-homogeneous ODE) supported by three solved examples in details.
Description: Reduction of order requires that a solution already be known. Without this known solution we wonβt be able to do reduction of order. Therefore, this file shows you the two cases of reduction methods ( homogeneous and non-homogeneous ODE) supported by three solved examples in details.