Ql: Find out whether each of the following functions is a solution of the ODE. (choose 1) p"(x) - 5p" (x) - 36p (x) = 0 or not. a) p(x) = cos(3x) - sin(3x) b) p(x) = 2sin (2x) + 3cos(2x)

Q: 1. f(x) = 2x2 – 3x+4 2. f(x) = e-2x sin 5x %3D

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Q: 3. Use the Intermediate Value Theorem to show that the following equation has a solution. sec(x) =…

A: Intermediate value theorem For a continuous function y = f(x) in the interval [a, b] such that…

Q: [Q2] Find a root of the function using the secant method with initial guesses of x-1 2 and xo 2.6.…

A: Introduction: A transcendental equation can be solved numerically. The base of solving a…

Q: Q2: Use the Newton-Raphson method to find a solution cos(x+ v2) + x+ vz) = 0, for-2sxs-1 accurate to…

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Q: b) [F(x) then find f(x). If 3 In(x)/ sin(3x) − 3e³ + x² + 3. - f(x)dx= 3 ln([x]) + 3x + C

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Q: 2x + 5 What is true about the function Ax) = X+3 as x → co?

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Q: Use Euler’s explicit method to solve the ODE dy/dx= -1.4 + 8e^ -0.3x from x= 0 to x= 2.4 with the…

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Q: .The action of a waterwheel can be modeled by the function y = 3 cos (T(x - 3) + 2). Within the…

A: Topic: maximum value of a function

Q: many

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Q: "(2) – 16f(2)) sinh(4x) dr Find the value of in terms of f(0) if f(a) = f'(a) = 0. %3D f(0) O f(0)…

A: See the calculation below  Fourth option is correct

Q: x2 Vcos(t) +3 at 1. COS 2.

A: Given that, the integral ∫2x2cos t + 3 dt

Q: -cosh(2x² + 1). Evaluate (A) 4xsinh(2x² + 1) B 2xsinh(2x²+1) C) xsinh(2x2 +1) с D (2x2 + 1)sinh(2x +…

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Q: Solve the ODE by the Euler method: given 2y" = -4y' - 1.5y y(0) = 3 and y'(0) = −2.5 with step h =…

A: To find- Solve the ODE by the Euler method: 2y'' = -4y' - 1.5y       giveny0 = 3 and y'0 = -2.5with…

Q: 3. Find the derivatives: 3x3-4 a) f (x) = b) y = (x2 + 6x + 2) (+ Vx5 + 3) DO NOT SIMPLIFY 2x²+3 c)…

A: a) Use quotient rule of derivative and find the derivatives of above function.

Q: The complementary function of (D² +4) y = 3 cos2x is О CF %3D Сј cos(-2x) + C2 sin(—2х) O CF = C1…

A: We need to find the complementary function . We have the function , D2+4y=3cos(2x)  Writing it in…

Q: L=2-36X, y'co) =5, and ylo)=S x)

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Q: 7 x5 dx, if f(x) = 3x-a 3x-b' ,for any real number a and b. If f (0) = 0 and f(1) is 20. Evaluate…

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Q: Classify the following ODE and solve the initial value problem y(1-x2)y' = xy2 - cosx.sinx , y(0)=2

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Q: 1. f(t) = -2e-14t + 5 Cosh(4t) 2. f(x) = 4 Sin(7x) + 480

A: We will use Laplace transform of some standard function to solve this.

Q: Evaluate D3(sinx – 4e) A cos x-32 ex B -cos x-32 e?x -sin x-32 ex sin x-32 e2x

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Q: 6) f(x) =xcos x 2n(-1)" • sin(nx) (n-1)(n+1)

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Q: 5. Solve the given ODE using the method of undetermined coefficients. y" − 4y = x² + 4x − 3 -

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Q: IV. Suppose z is a function of r and y, and tan Vy² + x² 2e&y¸ Solve for az az and dy

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: 1847 In x 5)- b) Show that the ode (x + tan-¹ y)dx + y dy = 0 is exact, then find the general…

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

Q: 2 Solve the following ODES by Inverse Operator method 1-2 ý -2y +y = e sinx ý tỵ X X Ans: y=c₁e +…

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Q: Question number 5

A: Given function

Q: Test the ff ODE for exactness and find the general solution of the DE. (2x + 3y) dx + (3x + 4y) dy –…

A: Let's find.

Q: Question3: A. Find the general solution of the following first-order ODE xy' = y + 2x³ sin² (²)

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Q: Q3) Express cos(x²) as a power series. а) 1. 2! + 6! 4! x10 + 3! x14 +. 7! b) 1– 5! c) 1– x5 x7 + 7!…

A: To express the function cos(x2) as a power series. Here, note that the power series of the function…

Q: - Verify whether the following ODE is exact and find its general solution. (2xy - sec²x) dx + (x² +…

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Q: Find the orginal function of this A Fx) =-1 (B) Frz)= X +1 ニー re Fez) s -x+3 tan x - sec3x

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Q: 3. Find 2 and 2 for the following: ду ax (а) f = e(2x+3y) -1 (b) f (x, y) = tan' (c) f = sin(2x² –…

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Q: 2. Obtain the general solution of the ODE (2a² – r²) dr = r³ sin 0 d0.

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Q: Consider the following ODE: y" = -4y where y is the dependent variable which is a function of the…

A: Given: ODE: y''=-4y General solution is given by, y=c1cos(2x)+c2sin(2x) To find the particular…

Q: Consider the following first-order ODE: x-y from x 0 tox 1.2 with y(0) -1 dx Solve using Euler's…

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Q: 1. Solve the following ODE using separable variable method: dy +(x+2)y³ =0. dx а)

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

Q: cos(3x) if x 1 if x = 0 or x = 1 3* if Let f(x) = 3 + In x if 3 Then f has removable discontinuity…

A: We will solve the following

Q: The complementary function of (D² +4) y = 3 cos2x is O CF = C¡ cos(-2x)+ C2 sin(-2x) O CF = C¡ cos2x…

A: Given a non-homogeneous differential equation, D2+4y=3cos2x. Consider the homogeneous equation…

Q: 21: Consider the ODE y = 2/y (a) Find the implicit general solution. COs x.

A: We will solve it using separation of variables technique.

Q: 12. If f(x)=sin(2x+1), then f'(x) is equal to A -2 cos (2x+1). 2 cos(2.x+1). 4 cos(2x+1). C D -4 cos…

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Q: Solve the given nonhomogeneous linear ODE by variation of parameters or undetermined coefficients.…

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Q: 1+ x² -L „tanx - for all x €[0,1/2], then f'(x) equals 1+ ex * If f(x) = sec2x A 1+ etanx sec³x B 1+…

A: Given an integral. We need to find f'(x).

Q: Q4. Solve the given ODE using the method of undetermined coefficients. - y" - 4y = (x² − 3)(sin2x)

A: Solution is below

Q: Solve for x(t) for the given ODE with initial values. x"(t) + 0.25x(t) = 0 with x(0)=3 and x'(0)-4

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Q: IV. Suppose z is a function of r and y, and tan y2 + x² = 2*e. Solve for az dz and %3D dy

A: To solve for dz/dy and dz/dx.

Q: 1. f(t) = cos(6t) 2. f(t) = (e^(8t)) cosh(3t) 3. f(t) = (t^2) e^(-4t)

A: Lcos(at)=ss2+a2 Leatcosh (bt) = s-a(s-a)2-b2 Ltneat = n!s-an+1

Q: Evaluate D6(cosx+e-2*) (A sin x +64e -2 B cos x – 32e-2r (c - sin x – 32e-2x cos x + 64e -2x |

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Q: Solve for the particular solution of the ODE y” + 4y’ + 3y = sin(e^x) a. yp = [e^(-2x)*sin(e^x)] +…

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Q: 3. Use the Intermediate Value Theorem to show that the following equation has a solution. sec(x) =…

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