Question

(c) Solve
au
дх
= 604 + u using the method of
at
separation of variables if u(x,0) = 10e​

Answer 1

Answer:

Step 1 Separate the variables by moving all the y terms to one side of the equation and all the x terms to the other side:

Multiply both sides by dx:dy = (1/y) dx. Multiply both sides by y: y dy = dx.

Put the integral sign in front:∫ y dy = ∫ dx. Integrate each side: (y2)/2 = x + C.

Multiply both sides by 2: y2 = 2(x + C)

Explanation: Dirichlet and Neumann boundary conditions are the two boundary conditions. They are used to define the conditions in the physical boundary of a problem.

The method for solving separable equations can therefore be summarized as follows: Separate the variables and integrate.

Example 1: Solve the equation 2 y dy = ( x 2 + 1) dx.

Example 2: Solve the equation.

Example 3: Solve the IVP.

Example 4: Find all solutions of the differential equation ( x 2 – 1) y 3 dx + x 2 dy = 0.