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greetings students and welcome back to another video on partial differential equations in this video weamp;#39;re going to derive the general solution of the wave equation but using an easier method thatamp;#39;s based on making a change of variables letamp;#39;s start by rewriting the wave equation up here just for our reference now what weamp;#39;re going to do is Define two new coordinates the first coordinate Iamp;#39;ll call R and the second coordinate Iamp;#39;ll call S R is just going to be x + CT while s is going to be xus CT what Iamp;#39;ll be doing here is converting our partial derivatives in T and X to partial derivatives in RNs and then weamp;#39;ll solve the resulting equation in RNs so letamp;#39;s begin we can use the chain rule to reexpress the partial derivative of U with respect to X in terms of the partial derivatives of U with respect to R and S like so we can also do the same for the partial of U with respect to T now letamp;#39;s use the definitions of
