the independency of the following solutions y1=sin x y2=4 sin x is Select one: O a. Basis O b. nonlineary dependent O c. independent O d. linear dependent

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A: Explanation of the answer is as follows

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A:

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A: (1) Given the function f1x=7x & f2x=2x2 we have to show that these function form a fundamental…

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A:

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A:

Q: 3t 台 = 2e 2セ %3D e

A: First lets put the values of theta in the equation

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A:

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A:

Q: (2) Use appropriate substitution to solve the following 1-1-y dy (i) dr tan (x+ v). (ii) y = %3D z+y…

A: As per our guideline we are supposed to answer only one asked question with first three subparts.…

Q: 5. Verify that the functions e, xe: form a fundamental set of solutions of the DE 4y" – 4y'+y = 0 on…

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A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: 47. Prove that the imaginary part of the solution of z" + z' + z = te' is a solution of y"+y' +y=t…

A: Given,                           z''+z'+z=teit                                 (1)

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A: follow next step

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A:

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

A:

Q: Given that the characteristic equation has the following roots, what is the complementary solution?…

A: We will find out the required complementary function.

Q: 18 In(z – 3) Question 10) Find I = -dz, where C = Iz - 2 + 4i| = 4, Ccw z2 + (4 + 4i)z + 3+ 4i

A:

Q: 3. ® Find the genelal Solution of the differentral egation (D'+ 25) y = cscX Sinx t Sin 5X cos 3X

A:

Q: Match the following guess solutions y, for the method of undetermined coefficients with the…

A: The detailed solution is as follows below:

Q: 4) Transform the parabolic equations (9)40xxt120xy けy-20x +0こo x+9 (6) e2x Uxx +2e**Jxy+ e®Uyy=O to…

A:

Q: Given that y1 = zi cos(z) and y2 = x¯i sin(z) form a fundamental set of solutions of z*y" + zy' + (z…

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Q: Q1:-/ Verify by direct substitution that y, = epx cos qx and y2 = ePx sin qx , are solutions of the…

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Q: eat cos(bt) C.

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Q: Derive the D'Alembert's solutiojn to the following Cauchy problem Un = Uxx, - 0 0 u(x,0) = e,…

A: Consider the Cauchy problem, utt=uxx, -∞<x<∞,  t>0ux,0=e-x, utx,0=sin2x, -∞<x<∞ We…

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A:

Q: If r(t) = cos(-5t)i + sin(-5t)j – 10tk compute r'(t)= i+ j+ k and fr(t) dt= i+ j+ k +C with Ca…

A:

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A:

Q: Find one particular solution to the following second-order forced equation d²y dy +8 + 15y = 5…

A:

Q: (b) Determine whether u(x,t)= e' sinx is a solution to L

A:

Q: b. Obtain the particular solution of the following dr =-4rt; when t=0, r =r, dt i.

A: Given: drdt=-4rt; when t=0, r=r0 For finding solution of given differential equation, we use…

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A:

Q: Given that the characteristic equation has the following roots , what is the complementary solution?…

A:

Q: Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the…

A: Given differential equation.y' = x+y2, y(0)=0,.we have to find y(0.2) .we use Euler's method…

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A:

Q: Consider the Bernoulli I.V.P ry'- x²y" = y, y(1) =1. where n-5. Let v= y" be the substitution that…

A:

Q: eBu – 1 eBau – 1 R(u) = 1B1 |u eBu + q – 1 + y2B2 u e$zu + q – 1

A: Given  Ru=γ1β1u-eβ1u-1eβ1u+q-1+γ2β2u-eβ2u-1eβ2u+q-1                  (i) To find a root of the…

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A: We need to solve the given differential equations:a) 2ydy=x2+1dxb)dydx-x2y2=x2c)4x2+16dydx=cosycoty,…

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A:

Q: Build the implicit scheme and the simplest iterative process for quasilinear equation ди Ət = * [ ].…

A: Given that: ∂u∂t=∂∂xku∂u∂x, ku=u0.6,0&lt;x&lt;x0t, 0&lt;t⩽2,ux,0=cosπx4, u0,t=ux0t,t=0. The…