a.Consider the differential equationis an integrating factor for the equation.[3 Marks](i) Find the inverse Laplace transform defined by a.Determineand classify the singular points of Legendre’sequation as regular or irregular.𝑑π‘₯+𝑦=0,)2π‘₯lnπ‘₯(iii)Solve the resulting exact differential equation. [4 Marks]𝑑𝑦(1βˆ’π‘₯𝑑π‘₯(i)Show that this differential equation is not exact.[3Marks]2+π‘˜(π‘˜+1)𝑦=0. [6Marks]𝑠2b. (ii)Prove that 𝑦𝑠2+25}[4Marks]βˆ’12𝑦{ℒ𝑑𝑦2βˆ’2π‘₯

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on Nov 24, 2024 at 1:38 am



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