Answer Happy

Subject :- Differential Equations
1. 2. 3. Solve the following first-order differential equation dy (x+1)+y=Inz. de subject to initial condition (1) = 10, Sketch the graph of f(2)=-z. 0<x<T, f(x) = f(x+2). Then, find the Fourier sine series of f(x). Given the following function Sketch the graph of even periodic extension of f(x) over-45 st. Hence, find the Fourier cosine series expansion for f(x). f(x)=², 0≤x≤2 f(x)=f(x+4). 4. By using separation of variables, show that the solution for the follow- ing heat equation with mixed boundary condition is given by du u Dr w(0,1)=0, a(z,0)=1. 0<=<1. w(z.)= 4 (2n-1) 0<x<1, 1>0, ,(1,1)=0, 1>0, sin 5. Consider the following heat equation the Of 2 05540, 1>0. (0,1)-0, ,(40,1)-0, 1>0, (2.0) sin (). 0<x<L Find the solution u(z, t) using the method of separation of variables by setting (2.1)= X(z)T(1).