13. Find the solution u(x, t) of the inhomogeneous wave equation UttUxx +1 on Rx (0,00) such that u(x,0) = u(x,0) = 0
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- Let c>0 be a constant. Solve the one-dimensional wave equation Uxx=(1/c^2)U 0<x<1, with the boundry conditions U(1,0)=U(0,t)=0, subject to the U(x,0)=3sin(3xpi)+4sin(4xpi) and Ut=(x,0)=0.(a) Solve the inhomogeneous 1st order equation Uz - Ut = cost U(x,0) = 0. (b) Solve the inhomogeneous wave equation on the real line Utt - ²Uzx = sin x, x ER U (x, 0) = 0, Ut(x, 0) = 0. Explain what theory you are using and show your full computations.(a) Solve the inhomogeneous 1st order equation U₂ - Ut = cost U (x,0) = 0. (b) Solve the inhomogeneous wave equation on the real line Utt- c²Uzx = sin x, x ER U(x, 0) = 0, Ut(x, 0) = 0. Explain what theory you are using and show your full computations.
- Solve the inhomogeneous wave equation on the real lineUtt − c2Uxx = sin x, x ∈ RU(x, 0) = 0, Ut(x, 0) = 0.Explain what theory you are using and show your full computations.(b) Solve the inhomogeneous wave equation on the real line Utt-c²Uzz = sin x, x ER U(x,0) = 0, Ut(x, 0) = 0. Explain what theory you are using and show your full computations.A string with motionless ends at x = 0 and x = 1 vibrates according to the wave equation Fu Ət² and the initial velocity J²u dr² 1. Use separation of variables (show details) to solve the equation provided that the initial profile of the string is u(x,0) = 4 sin(2x) Ju 5- Ət It=0 = 0.
- (a) Solve the inhomogeneous 1st order equation Uz - Ut = cos t I U (x, 0) = 0. (b) Solve the inhomogeneous wave equation on the real line Utt- c²Uzz = sinx, x ER ᏆᏆ U(x, 0) = 0, U₁(x, 0) = 0. Explain what theory you are using and show your full computations.a²u Solve the wave equation: at² - 02.02 0x2 Under the condition: u=0 when x = 0 and x = π Du =0 when t= 0 and u(x, 0) = x², Ət 0