The function y=C, e° is the general solution of a) O y"– 2 y' – 3 y = 0 b) O y" +2 y' – 3 y= 0 O y" + y' + 3 y= 0 d) O y" – y'+ 3 y = 0 e) O y'+ 2 y = 0 f) O None of the above.

Q: 8y'' - 12y' + 5y = 6 cos t

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Q: The solution of: v(t) = e =t + ] sin(t - T)y(T)dt , in terms of convolution is:

A: Convolution theorem of Laplace transform    Laplace transforms of the functions Inverse Laplace…

Q: - Determine the largest interval in which the unique solution of (t – 3)y +tan t y =t, y(n) =0 is…

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Q: A rectangular steel sheet is bounded by the axis x 0,y = 0,x = a and y b. The temperature along the…

A: pleas see the next step for solution

Q: Find a particular solution to the IVP given by: y" + 2y" - y' - 2y = 0, y(0) = 1, y'(0) = 2, y"(0) =…

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Q: sa (0, ") : If f(1, y) = 18e* cos z + 5 cot y, then the total differential of f at (0, O df = 18 dr…

A: Total derivative

Q: Find the solution u(r, t) of uz = }utt, 0 0, which satisfies the boundary conditions u(0, t) = u(3,…

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Q: If u = x? + y? + z?, where x = e2t, y = e2t cos (3t), z = e2t sin (3t), %3D du at t= 0 is dt then

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Q: a1/ Find c; and ey so that ytx) = c; sin x +cz cos x will satisfy the given conditions. Determine…

A: Note: Since you have asked multiple question, we will solve the first question for you. If you want…

Q: dz Use an appropriate form of the chain rule to find dt 1 z = 4 cos x – sin xy; y = 7t || Enter the…

A: We have to find

Q: Obtain the DE given the general solution . y = c, + C,x + C,x³ + (c, +c,x)e~Và« + (cq cos 2x + c,…

A: We will generate auxiliary equation from the roots of it

Q: A rectangular steel sheet is bounded by the axis x = 0, y = 0,x = a and y = b. The temperature along…

A: Solve the problem according to conditions

Q: Solve the Neumann problem Ди — 0 Uz(0, y) = 0, Uz(7, y) = D, cos(ny) Uy(x, 0) = 0, u,(x, T) = 0 0 <…

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Q: 3. Solve the equation u, for x E (0, L) and t > 0, - dx2 for the following boundary conditions: u(0,…

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Q: The IVP whose solution is y=2e-Xcos(x)+ 3e¬*sin(x) is given b O d. y"+2y+2y=0, y(0)=2, y(0)=-1. O a.…

A: Introduction: Calculus is a branch of mathematics that focuses on rates of change, differential…

Q: The longest interval in which the 1.V.P y" +(tanx)y- xy = x, y(1) = 3, y'(1) =0 surlay has a…

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Q: A rectangular steel sheet is bounded by the axis x = 0, y = 0,x = a and y = b. The temperature along…

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Q: 2. Used Euler's method to approximate y (0.5) and y (1) for the I.V.P y' = y + xe2x, y(0) = 1.

A: Given y'=y+xe2xand y0=1

Q: If u(x, t) = D1 fn(t) sin(nx) is the solution Utt – 9ura = 2e2t sin(3x) + e-2t sin(4x) u(0, t) = 0 =…

A: Given: ux,t=∑n=1∞fntsinnx is the solution of the PDE…

Q: Show that xo = 0 is a regular singular point of the equation xy" – 5 - +x ) y' + 3y = 0). Determine…

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Q: There exists a solution, F(x,y)=Dc, to (2- 2aye) da – (2ye + 3 sin y) dy = 0 such that - OF 2ye 3…

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Q: The solution of ë+w?x = fsin wt with initial conditions r(0) = 0 y a(0) = 0 is given by %3D %3D

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Q: A rectangular steel sheet is bounded by the axis -0y-0,x-a and y b. The temperature along the edge…

A: Steady state heat equation.

Q: (d) Using the method of characteristics, or otherwise, find the general solution to yu, – x*u, = 0,…

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Q: Use the method of separation of variables to solve :=0 in (0,1) × (0,+0), (2) u(0,t) =u(1,t) =0,t…

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Q: The equations xcos(u) + 9uy2 + e² + 2 = 0 and 3ye" + 4x²v – 3æcos(2) +1 = 0 are solved for u and v…

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Q: Find the solution u(x, y) of u+sin(r) uy = y for z, y ER, u(x = 0, y) = 0.

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Q: 3- Find the solution of y" + y= sec (x) a) y(x) = c1 cos x + c2 sin z sec z + sin Cos z sin" z b)…

A: Given is the second order linear ordinary differential equation.

Q: 6. Find the solution u(r, t) of u = tut, 0 0, which satisfies the boundary conditions u(0, t) =…

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Q: х. у 2) w=¨+2,x= cos“(t), y = sin°(1), z =-, at t = 3 Z Z t

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Q: The IVP whose solution is y= – e*cos(x) + e*sin(x) is given by Ocy-2y +2y=0,y(1) = e",y(pi) =0 O d.…

A: To find the IVP for the below solution.

Q: dz Use an appropriate form of the chain rule to find dt 1 z = 9 cos x – sin xy; x : y = 4t t' Enter…

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Q: dz Use an appropriate form of the chain rule to find dt 1 z = 6 cos x – sin xy; x = y = 6t t' Enter…

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Q: A rectangular steel sheet is bounded by the axis x = 0, y = 0, x = a and y = b. The temperature…

A: Answer is given below

Q: ди Әх and initial condition ди + + u = 0, x > 0, t > 0, Ət olve u(0,t) = 0 t > 0, and u(x,0) =…

A: Given That : ∂u∂x+∂u∂t+u=0 ,x&gt;0,t&gt;0u(0,t)=0 ,u(x,0)=sinx To Find : Solution of the Partial…

Q: 3- h(x, y, z) = cos xy + e*y + In zx, Po (1,0,1/2), A = i + 2j + 2k

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Q: dz Use an appropriate form of the chain rule to find dt 1 z = 9 cos x – sin xy; x y = 2t t' Enter…

A: This question is based on Derivative.

Q: 7. Suppose that f (x, y) = e" cos TY and u? – v², y = u? + v?. x = Using the chain rule, compute the…

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Q: 4. An imaginary ant is walking on an imaginary cartesian plane so that at any point (x, y) it moves…

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Q: 3. Given: y = f (u) and u = g(x), find dy/dx: a) у%3D сos u, и%3D—х/3 b) y = tan u, u = 10x – 5 - с)…

A: Our aim is to find the derivative of the above expressions.

Q: 8. Let f(x, y) = cos(y – x) and r(t) = (e', e2t). Find if (r(t)) at t = ln(3).

A: The solution is given as

Q: Show that xo 0 is a regular singular point of the equation %3D xy" + + x ) y' – 4y = 0. Determine…

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Q: dz Use an appropriate form of the chain rule to find dt 1 z = 8 cos x – sin xy; x = y = 2t t' Enter…

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Q: (d) Using the method of characteristics, or otherwise, find the general solution to y-uy – xu, = 0,…

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Q: Find a general solution to (x' +xy')y' = y implict form F(x, y)= C : Give an

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Q: Let y= a,+a,t+ azt? + a3t³ + a4t* + agt5 + agt6 +...... be the solution of d?y ад dy +t- +y=tan-'t ;…

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Q: If u(x, t) = E1 fn(t) sin(nx) is the solution Utt – 9uzz = 2e2t sin(3x) + e-2t sin(4x) m=1 u(0, t) :…

A: Given: ux,t=∑n=1∞fntsinnx is the solution of the PDE…

Q: dz Use an appropriate form of the chain rule to find dt 1 z = 8 cos x :- sin ry; y = 9t Enter the…

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Q: The longest interval in which the I.V.P y" + (tanx)y-xy x, y(1) = 3, y'(1) = 0 surlay has a solution…

A: Given,  y''+tanx y'-xy=x It is of the form,  y''+p(x) y'+q(x) y=g(x)