a. Determine the characteristic curve of the following second order partial differential equations and state whether...

 

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a. Determine the characteristic curve of the following second order partial differential equations and state whether it is parabolic, hyperbolic or elliptic. i. -Uxx +xU₂ + y²U = U+Ux ii. (1+x²)U+U+(1+y²) U=U₁ b. Use the method of separation of variable to obtain a solution of the wave equation cUxx=U₂ On the interval xe [0.L] subject to the conditions that in (27x) u₂(x,0) = 0. c. i. In Fig. 1 illustrate RL circuit, determine the relationship between the input and out of the circuit where E. R and L have their usual meanings. ii. Name the equation derived in Q2c (1). Tx u(0,t)=0, u(L,t)=0, u(x,0)=sin +sin 00 L W Fig. 1 a. Determine the characteristic curve of the following second order partial differential equations and state whether it is parabolic, hyperbolic or elliptic. i. -Uxx +xU₂ + y²U = U+Ux ii. (1+x²)U+U+(1+y²) U=U₁ b. Use the method of separation of variable to obtain a solution of the wave equation cUxx=U₂ On the interval xe [0.L] subject to the conditions that in (27x) u₂(x,0) = 0. c. i. In Fig. 1 illustrate RL circuit, determine the relationship between the input and out of the circuit where E. R and L have their usual meanings. ii. Name the equation derived in Q2c (1). Tx u(0,t)=0, u(L,t)=0, u(x,0)=sin +sin 00 L W Fig. 1

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