Biomedical Engineering > GATE 2024 > Differential Equations
Consider a system of the following two partial differential equations:
(∂α/∂x)=-2(∂β/∂t)
(∂β/∂x)=-2(∂α/∂t)
Which one of the following choices is a possible solution for the system?
A
α(t,x)=(x-t)^2+(x+t)^2 and β(t,x)=(x-t)^2-(x+t)^2.
B
α(t,x)=(x-2t)^2+(x+2t)^2 and β(t,x)=(x-2t)^2-(x+2t)^2.
C
α(t,x)=(x-(t/2))^2+(x+(t/2))^2 and β(t,x)=(x-(t/2))^2-(x+(t/2))^2.
D
α(t,x)=(x-(t/2))^2+2(x+(t/2))^2 and β(t,x)=2(x-(t/2))^2-(x+(t/2))^2.

Correct : b

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