Word Count : 358

---

We solve the partial differential equation (PDE) using the separation of variables method. ### Given PDE: \[ \frac{\partial u}{\partial x} = 2\frac{\partial u}{\partial t} + u \] with the initial condition: \[ u(x,0) = 3 e^{-3x} \] --- ### Step 1: Assume a Separable Solution We assume \( u(x,t) \) can be written as a product of two functions: \[ u(x,t) = X(x)T(t) \] Substituting into the PDE: \[ \frac{d}{dx} (X(x)T(t)) __________ __________ ___ ________ ___ ________ ______ __________.
_________ ____ ________ ________ _______ _____ __________ _________ _______ ___ ___ _________.
__________ _______ ___ ____ _________ _________ ___.
__________ _________ ______ ____ _________ ________ __________ _________ ________ ____.
___ __________ _______ ________ ___ _____ _______ _____.
___ _________ __________ _____ _____ _________.
________ _____ _________ ________ _____ ________.
_____ _______ __________ __________ ______.
_______ _________ _______ _____ ____ ______ _________.
_______ _________ ________ _________ ___ ________ _________ __________ _______ ________ __________.
_______ _____ ____ _____ _____ _________ _____ ______ _______ ____ ____.
____ ______ ___ __________ _________ _______ ____.
________ __________ ___ _____ ____ _______ ___.
_______ ____ _______ _______ _______ _______ ____ ______ _____ ____.
________ __________ _________ __________ _________ ____.
__________ ___ _____ _____ _________ _______ _______.
___ ______ __________ _______ __________ _________.
__________ ______ _______ ____ ____.
_______ ______ __________ _____ _________ ___ _______ __________ _________ __________ ___ __________.
___ ___ _______ ____ _________ ___ _____ _________.
__________ __________ _______ ____ ___ ______ _____ __________ __________ ___.
________ ____ __________ ____ _______ ________.
____ _____ _______ _______ _________ ______ _____ ____ ________ _________.
_________ ______ _________ _________ ______ _______.
_____ _______ ______ ___ ___ ____ _________ __________.
______ __________ ____ _____ _________ _____ ___ _______ ______ __________ ________ __________.
___ _________ ______ __________ _______ ___.
_____ _________ _______ ____ _________ _________ ______ ______ ___ ___.
__________ _____ _____ ____ ___ ________ ________ __________ _________ ______ ____ ___.
_______ ____ _________ ___ _____ _______ _____ ___ ___ ______ ______ ____.
____ _________ _______ _________ ______ _____ __________ ___.
_________ ______ ________ ______ __________ _________ ___ __________ ___ _________ _______ _________.
______ _____ ___ ______ __________ __________ ______ __________ _____ _____ ___ _________.
________ _______ _____ ____.
Get Full Answer on WhatsApp