Solve the eigenvalue problem Lf (x) = Af(x), where k df(x) i dx In the region -a < x< a, subject to the boundary condition that f (a) = f(-a) Lf(x) = – ßxf (x) -

Q: If f(x) = f'(x) = 1 x³ 3 √t² + 1 dt then F

A: Here we will use the Leibniz theorem to  find the derivative of the given problem, so on using this…

Q: For problems # 1 - 5 show the Laplace Transform for the given function is what the chapter states…

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Q: Consider the initial-value problem y' = x + 2y -1, y( 1) = 2. a) Find the analytic solution.b)…

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Q: Show that P2(x) = f(a) + f'(a)(x − a) + c2(x − a)2 for each value of c2 satisfies the requirements…

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Q: A certain species of puffins lives in Nova Scotia. The population dynamics of this species is…

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Q: (7) Find the local linear approximation of f(x) = √2+3 at zo = and use it to estimate the val of…

A: The linear approximation of function f(x) at  is The given function is

Q: 1 Integrate with respect to x. 4+ 25(3x +1)²

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Q: f(x) In(x² – 6)' at X = +2

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Q: Determine the value of the Wronskian W(y1, y2) of y" - 2y + 1 = e2*(x + 1) if x-0.2 by using…

A: Given, y''-2y'+1=e2xx+1. The objective of the problem is to obtain the value of the Wronskian if…

Q: T: P2---&gt;P2 defined by T(p(x)) = p(x) + p' (x)

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Q: (b) Find the Wronskian W[y1,Y2](t) of y1 and y2-

A: W[y1,y2]= -t2et

Q: f"(x) = 20x3 + 12x2 + 4 with the initial conditions f(0) particular f(x). = 8 and f(1) = 5. Det

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Q: 8. Find f(4) if f(0) >0 and [f(x)]² = [(f(t))² + (f'(t))²]dt + 4.

A: We do this using Lebniz rule for differentiation under integral sign. The detailed solution is…

Q: Derive the numerical integration for Boole's Rule given by b- a | f(x)dx= l4(f) = [f(a) + 32f(x1)+…

A: Substitute n=4 in the general formula for solving numerical integration to obtain the expression of…

Q: Find all FIRST and SECOND order critical POINTS for f(x) = (x² +x – 2)'/3

A: fx = x2+x-213f'x = 13x2+x-213-1 . ddxx2+x-2        = ddxx2+ddxx+ddx-23x2+x-223        =…

Q: Solve PDE 1 = e=*t u. u̟ =e¯*t Xx k (o0) u(0,t) =0 u(L,t) = 0 u(x,0) = L -x?

A: The given PDE is,uxx-1kut=e-xt

Q: y=A x ln(x) + B x + F is the particular solution of the second-order linear DEQ: xy'' =8 where y'=2…

A: the solution of the given problem is below...

Q: Solve the separable I.V.P y' (x2 +1) = x (y² + 4), y(0) = 0. y = 2 tan(2 + In(x + 1)) y = 2 tan(In(x…

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Q: Consider the IVP dy = (). Iy(20 -- y), y(0) = 1. dt %3D (a) Solve the IVP, finding y explicitly as a…

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Q: 12:06 ■I 5G (8) If f(z) = √1+dt and g(y) = f (x)dx then find g"(#/3).

A: Thank you

Q: Let y₁(x) and y₂(x) be any two twice differentiable functions, not necessarily eigenfunctions, in an…

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Q: dt, then F'(x) = 0 a) If F(x) = √5 / / di 20 3 b) If F(x) = ² = dt, then F'(x) = c) If F(x) = √²/1/1…

A: Given:   a) Fx=∫20x1tdt      we use common integral ∫1tdt=lnt          =lnt20x          Fx=lnx-ln20…

Q: f(3) = 5, g(3) = -4, f'(3) = -2, g'(3) = 7, f'(5) = 3, g'(5) = 10 a) If h(x) = f(x)g(x), find h'(3).…

A: topic - functions and derivatives

Q: Let u = f+cK* u with c real and K(x) = H (x)be-bx, b>0. (a) Find the general solution.

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Q: If f (x, y) = V3 + y³ In (z +y°)e*in(zyty") +2² + 10y , then fz (1,0) = |3D %3D O 2 4. O 3

A: Given that fx,y=x3+y33lnx2+y2esinxy+y2+x2+10y3 First we have to find fxx,y where fx=∂f∂x