How to solve pde ut+aux=e^(-2x), u(x,0)=f(x)

Introduction : In this solution we explain step by step the method How to solve pde ut+aux=e^(-2x), u(x,0)=f(x). Question: solve pde \[u_{t}+au_{x}=e^{-2x}\] subject to initial condition \[u(x,0)=f(x)\] Solution: Given pde \[u_{t}+au_{x}=e^{-2x}\] \[u(x,0)=f(x)\] So the parametrizing the curve as \[Γ=(s,0,f(s))\] Now…

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