4.2 Find the solution subject to the following boundary and initial conditions of the heat equation, u = a²uxx- (a) u(0, t) = u(1,t) = 0, u(x,0)=z,0
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- Verify that any function of the form Y (t) = c1vt + czt* satisfies the equation ty"(t) – ĮtY'(t) + 2Y (t) = 0. Determine the solution of the equation with the boundary conditions Y(1) = 1, Y(4) = 2.3. Consider the heat equation du Pu k for 0 0 with the boundary conditions du -(0, t) = 0 and ди (L,t) = 0, for t> 0. Solve for the following initial value conditions: a) f(x) = 2+ 3 cos 3TT) L (1 0€ (0, L/2] b) f(x) = 2 1 (L/2, L)3
- part A and B solutio needed urgenty4.2 Find the solution subject to the following boundary and initial conditions of the heat equation, ut = a²uxx- (b) u(0, t) = u(2,t) = 0, u(r,0) = 1 if 0Show the complete solution for this force vibration without damping equationHelp me understand betterSolve the following IVP. 2y" + y' + 2y = g(t), y(0) = 0, y'(0) = 0 where 5 st< 20, g(t) = 0 st< 5 and t 2 201 ' The solution of the heat equation wzz =wt, 0Use the method of separation of variables to find the general solution of the following partial differential equation du Ju Ət - u subject to the initial condition ?х u(x,0) = exFind the dependent, independent, derivatives, ordinary/partial, order, degree, linear or non-linear, general solution, p[atrial, solution and singular solution.Find a general solution to each linear ODE, and then find the specific solution with the given initial condition by using the integrating factor (a) u'(t) = u(t)+3, u(0) = 3 (b) u'(t) = 2u(t)+4, u(0) = 0 (c) u'(t) = −3u(t) +3, u(0) = 5 (d) u'(t) = −3u(t) +9t, u(0) = 5 (e) u' (t) = u(t)+2sin(t), u(0) = 1 (f) u'(t) = −4u(t) + e¹, u(0) = 2 (g) u'(t)= tu(t)+t, u(0) = 2 (h) u' (t) = u(t)/t+2, u(1) = 3 (i) u' (t) = sin(t)u(t) + sin(t), u(0) = 4 (j) u' (t) = au(t) +b, u(0) = uo, where a, b, and uo are constantsSEE MORE QUESTIONSRecommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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