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hi there welcome to my videos on Elementary differential equation this is video number 10 for chapter nine the topic is partial differential equations in this video we will take another look at the wave equation and derive the solution for that using a completely different method and the method was due to the lamber and this solution is called the limbo solution of wave equation so lets consider our wave equation in one space Dimension u t t equals c Square u x x so we now claim that the two functions U1 and U2 as follows U1 function of x and t equal to some function Phi depending only on one variable that is X Plus CT and the second function U2 lets call it PSI its just a name for the function and that PSI function now depends only on the variable x minus CT okay and we claim that and the two functions like this for any arbitrary functions V and PSI would be solutions for the wave equation and then if that is true then by the principle of superposition the sum of these two will al