Solutions to Engineering Mathematics Vol - III

a₁ analytic auxiliary equations b₁ C.R. equations c₂ sin px Cauchy Integral Formula Cauchy Integral Theorem Cauchy Residue Theorem complete solution Consider cosh cosine series d²y dx dy dy dx Equating the co-efficient f₂(y Formula Fourier half-range sine function given differential equation given equation half-range sine series Hence Inverse Laplace Transform J₂ Let f(x linear partial differential Method Multiplying nx dx odd function P₁(x partial differential equation pole Put A.E. regular singular point required Fourier series required solution s²+1 sin x sin² sinh solution is given Solve Taking Inverse Laplace w-plane x+2y απ ηπ ηπ ηπ ηπα π π πα дг ди дх дх ду пп ппх