Question 3. Find the general solution of the following ODE: a²y" - 4xy +6y = 4x° In(x), r> 0.

Q: Question#03 Solve by any appropriate method. x*y" + 2r'y"-xy' + xy = x*sin(Inx) Question#04

A: 3. we have given equation  x4y'''+2x3y''-x2y'+xy=x2sin(lnx) ...(i)    now divide equation (i)  by…

Q: Question 2. Use Frobenius method to find the solutions of the following ODES 1. ry" +y' – 12y = 0

A: Given: The differential equation is xy''+y'-12y=0.

Q: Question 4 -e-*) dx Evaluate: A '+C 2 B cosh x +C sinh x +C D – sinh x +C E None (F -cosh x +C 2

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Q: Question No.4 Laboratory department detects the concentration C of impurity of an oil purifier…

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Q: Question 10 Given z = (e-22) (sin y), find 92 O-2e-2 O-2 e 2 (sin y) + e-2 (cos y) O-2e-2 (sin y) -2…

A: We have to find derivative of given term.

Q: Question 2. Find the general solution of the given ODE for t > 0, t²x" − t(t+2)x' + (t + 2)x = t³e¹.…

A:

Q: QUESTION 2: Test for exactness, and solve the Initial Value Problem for the following first-order…

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Q: Question no 3: if an ODE is given as (x +x +1)dx +(y² -y +3)dy =0 with y(0) =1 Find the numerical…

A: given ODE is                                              x2+x+1dx+y2-y+3dy=0, y(0)=1, h=0.1 so,…

Q: Question 2. Find all functions A and B such that the following equations are Exact. Do Not solve the…

A: A equation is exact if it satisfies differential, df=0 Explanation follows

Q: QUESTION 4 x' = 12 t2 x, x(0) = 3 Solve the above IVP and then find x(0.5). Put x(0.5) accurately…

A:

Q: Question 7 10 fx)dx into To use Gauss quadrature formula we have to convert 2.5/2.5+7.5x) dx 7.5…

A: Given: The integral  ∫510f(x) dx

Q: Question 3 z+3 dx Use the substitution u = 1 - 2. 1 O sec I|+3 sin x+C OIn(1 – a) + 3 sin-1 a + C…

A:

Q: Question 4: Solve the equation ë + 6¢ + 8x = g(t), where g(t) is an impulse of 4 units applied at t…

A: Lxt=Xs,L-1Xs=xt d2xtdt2=s2Xt-sx0-x'0dxtdt=sXt-x0 L-1Xs=xtL-11s=1L-11s-a=eat x¨+6x˙+8x=gtx0=0,x˙0=3…

Q: Question 3 of 12 Find the general antiderivative of f(x) = 4 cos (x) - 7 sin (x) and check the…

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Q: Question 9 Given f(x, y, z) = zey 0 0 01- 02-/ O 2e² - 3 Onone of the choices - X sin (#), what is…

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Q: 1-S Ca-メ)xde

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Q: Question#1(a): Solve the following ODE by Heun's method, y(1) = y - y sint, 2 <t<3, y(2) = 2, h=…

A: This method can be used to simplify the differential equation by providing primary values. Here, the…

Q: Find if y = cos(e-2=) dy None 2e-2". sin(e-2") 3e2r. cos(e-2r) e2= . sin(e-2#)

A:

Q: Can you please answer this question and show all of the steps and say the correct letter

A: Given function is

Q: Question 5 Determine a suitable form of a particular solution yp if the method of undetermined…

A:

Q: Question 2: Find the solution of the given DE (2xy cos(x?) – 2xy + 1)dx – (sin (x²) – x²)dy = 0

A: The given question is taken from the calculus in which we have to find the solution of the given…

Q: Question 2. Find the general solution of the following ODE: y" – 4y' + 4y : I > 0.

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Q: Question 12 Evaluate: f 0 tan (0)d0 O E arctan 0 + arctan(0) 0 +C 21 O arctan(0) 0 2 arctan 0 + C 21…

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Q: Question 28 F(x) = | " dt is equal to 65612 You Answered None of the given choices Correct Answer O…

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Q: QUESTION 11 The first approximation(p) of the root of the equation f(x) = /x- cos(x) = 0 by Newton…

A: Newton-Raphson method (also known as Newton's method) is a way to quickly find a good approximation…

Q: Question 003: Complete the following question involving Substitution Method. Given the integral S8…

A: Given : ∫8sin3x-7cos3x-75dx

Q: Question 9 | xe*dz. Evaluate Choose 1 answer: A O -e(x – 1) + C

A:

Q: Question 1. Find the general solution of the following ODE: y" – 4y' + 3y = -6e² + 40 sin z.

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Q: Question (3): Test for exactness and solve the following 1st order linear ODE: (a + 1)y + (b + 1)x…

A:

Q: Question 2 of 9 Solve using the method of undetermined coefficients: x" – x' = te";x(0) = 2,x'(0) =…

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Q: QUESTION 3 x" +5x' + 4x = 12t + 30 e, x(0) = 1, x'(0) =3 Solve the above IVP and then find x(0.25).…

A: The given differential equation has been solved in step 2 and step 3.

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

A:

Q: Question no 3: if an ODE is given as (x² +x +1)dx +(y² -y +3)dy =0 with y(0) =1 Find the numerical…

A: given equation is                                                x2+x+1dx+y2-y+3dy=0y(0)=1, h=0.1 we…

Q: 1. For each of the following equations, eliminate the constants A and B to form an ODE. y = Ae³* +…

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Q: Question 02: Solve with suitable condition d'y dx - = 0, where y(0)=2, y'(0) = 3, y" (0) =4, y" (0)…

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Q: dx 3xy' + y + x2 y4 = d

A:

Q: Question 2. Find all functions A and B such that the following equations are Exact. Do Not solve the…

A:

Q: Question 5 Does x2 – 10 = x x sin x have a real solution? Show your process. %3D

A: yes the equation have real solution

Q: Question no 3: if an ODE is given as (x2 + x + 1)dx + (y² – y + 3)dy = 0 with y(0) = 1 Find the…

A:

Q: H.w: Solve the following of the first ODES: dy 1- dx 1 y = x |

A: According to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Question 001: Complete the following question involving Substitution Method. Given the integral 2x +…

A: Given:∫e2x+7dx

Q: I== (0),” 0=(0)," I-= (0)" 0="pt8tstan

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Q: Question 20 Solve (x + Vy² – x²) y' – y= 0 O '(÷) - In y - sin O None of the choices O In y – sin )…

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Q: QUESTION 4 SIn(x +2) dx = O A (x +2) In(x+2)- 20x +C O B. x In(x + 2) 20 " -x+ C 20 OC (x +2) In(x…

A: Integrated by part

Q: Question 3 What is the general solution to the DE, = 2? – 2x + 2? What is the general solution to th…

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Q: Question 2. Find the largest interval of existence and uniqueness of solution for the IVP 1 tx" +…

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Q: Question 1 xcos (2r²+7 )dx A -sin (2x²+ 7) + C B 4sin (2x²+ 7) + C B - 4sin (2x²+7) +C D - sin…

A: Given :∫xcos(2x2+7)dx

Q: the following equation is exact or not. If exact, obtain the General Solution to the following ODEs.…

A:

Q: QUESTION 3 a) Evaluate |x2 In | x+1| dx by using integration by parts. b) Use the trigonometric…

A: We apply integration by parts and evaluate the given integration. For part (a) follow 2nd and 3rd…

Q: Question#1(a): Solve the following ODE by Heun's method, y'(1) = y? - y sint, 2<t < 3, y(2) = 2, h =…

A: Here the solution is by Heun's method (Improved Euler's method) is as follows :