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Consider the following differential equation

\[
\frac{\partial y}{\partial x}=3 \frac{\partial y}{\partial t}+y
\]
If $y(x, 0)=10 e^{-2 x}$, then the solution of the differential equation is

  1. $y(x, t)=10 e^{-2 x-t}$
  2. $y(x, t)=10 e^{-2 x+t}$
  3. $y(x, t)=10 e^{-2 x-2 t}$
  4. $y(x, t)=10 e^{-2 x+2 t}$

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