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The partial differential equation
δu + u δu = δ2u is δt δx δx2
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- linear equation of order 2
- non-linear equation of order 1
- linear equation of order 1
- non-linear equation of order 2
Correct Option: D
Order is index of a derivative present in a PDE (i.e.) maximum there.
Hence, | ⇒ highest index 2 ⇒ order = 2 | δn2 |
if y, y2 solution of a PDE, then PDE is linearly independent.
+ | = | ......(1) | ||||
δt | δx | δx2 |
+ | = | ......(2) | ||||
δt | δx | δx2 |
If y = ay1 + a1 y2 is a sum of the PDE
(ay1 + a1y1) + (ay1 + a2y2) | (ay1 + ay2) = | (ay1 + ay2) | ||||
δt | d2 | d22 |
Hence PDE is non linear of order 2