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First, let us find the solution of the homogeneous equationy′+xy=0We get,y′+xy=0⇒y′=−xy⇒dydx=−xy⇒dyy=(−x)dxBy integrating both sides, we get,∫dyy=∫(−x)dx⇒ln(y)−x22+ln(C)⇒log(y)−log(C)=−x22⇒(yC)=−x22⇒y=Cex22So, the general solution of the given differential equation is given byae−x22+e−x22∫exe−x22dx
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Find Laplace Transform of each following
(a) tn , (b) cosωt
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