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1. Given the following initial value problem: 6y =0, y(0) =...

1. Given the following initial value problem: 6y =0, y(0) = 5, , y'(0) = -9. (1) Consider a series solution of (1) of the form 00 y(x) = [ an xn . n=0 (a) (8 points) Determine a recurrence relation for the coefficients an. (b) (9 points) Determine the series solution to the initial value pro...

I need you to solve this linear, first - order differential...

I need you to solve this linear, first - order differential equation for T(E). You can use a computational program like Mathematica, Maple, etc. : cu/dI(E) ) + XT(E)CVP = I 2 (de Po E + 2 T where T = stress = PC2E * C and S are (1-SE)2 constants Cv = constant volume specific heat E = stra...

1-4 Solve the given initial value problem using the method ...

1-4 Solve the given initial value problem using the method of Laplace transforms. 1. y" '-4y=1,y(0)=4 y(0)=0 - = = y"+3y" +3y'+y=0,y(0)=-4, y(0)=4,y"(0)=-2, = = (s) = -4s²-8s 2 2. (s+1) -st+s-1 3. y"-3y'+ 2y y(0)=0, - = cost, = 4. y&qu...

Need to show the calculation process of linearizing these fu...

Need to show the calculation process of linearizing these functions: Eqns: 8p 0(pv) = 0 Ot + Ox Ov Ot + Ox Ov = ) + [V(p)-V/ T - + 1 a (MON ar par N = I' p(x,t)dx=phL Boundary condition q(0,1) = q(L,t), v(0,t) = 00/0r/L. in the neighbourhood of the homogeneous state: P = with respect to t...

1. Consider the nonlinear system of difference equation = 1...

1. Consider the nonlinear system of difference equation = 1 x(n) (1) , a) Use the method of Lyapunov functions and put a condition on a so that the equilibrium solution x* = 0 of (1) is asymptotically stable. b) Let a = 1 and B = 11/ in equation (1). Find all the critical points and study thei...

Question 1 1 pts If R. = 8.0 n and the battery voltage Vo ...

Question 1 1 pts If R. = 8.0 n and the battery voltage Vo = 21.0 V, what is the current in the 2R resistor ? Module R + R 2R R V0 0.938 A 0.625 A 1.31 A 0.375 A 0.525 A Question 2 1 pts Two large conducting parallel plates A and B are separated by 2.4 m. A uniform field of 1500 V/m,...

7. Forced vibrating string with Dirichlet boundary condition...

7. Forced vibrating string with Dirichlet boundary conditions: (a) Consider vibrations of a string subject to an external force f(x,t). - = 0 < x < L; t > 0 u(0,t) = 0, u(L,t) = 0 t > 0 . u(x,0) = = (x) 0 < L Solve this by using the eigenfunction expansion met...

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