Consider the non-homogeneous O DE y +2 y +2y = sin 2x using undetermined coefficients method, the form of Ye is CA Yp = x(C, cos 2x + Cz sin 2x} %3D 08 Yp = C cos 2x+ Cz sin 2x Oc e = e( C cos 2x+ C2 sin 2x ) 0o o = x?(C, cos 2x+ C2 sin 2x )

Q: Determine the general solution on the given D.E. by using Separable Method: sin a sin y de + cos a…

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Q: 4 3 12 2 cos (x2) 3Vz Evaluate the integral|| dx dy dz by changing the order of integration in an…

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Q: The Particular Integral for the Euler Cauchy Differential Equation d²y dy is given by - 5x + 9y = x5…

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Q: 1. Verify that y = 3e-2x + 4x³ In x is a solution of y" – 4y' + 5y = 0 Obtain the general solution…

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Q: Find the solution of the heat conduction problem 0 0; 100uxx = Uti u(0, t) = 0, u(x, 0) = sin 3rx –…

A: Detailed explanation mentioned below

Q: ⌠31 (e0.5x + sin2x) dx. use n=4 ⌠41 cosx(0.25x2 + 1.90)dx, use n=3

A: As you didn't mention any question, we will only answer the first parts of these questions. Please…

Q: 5 Evaluate the integral 2x cos(xy)dydx 4 0.

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Q: Express the solution of the given initial value problem in terms of a convolution integral y" + 12y'…

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Q: What is the general solution of (D® + 20Dª + 100D2) y = 0 Oy = C + C2x + (C3 + Csa) cos 10r + (C4 +…

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Q: Use Secant method to to approximate the solution of f(r) = z+ cos z =0 accurate to within 10-3,…

A: The secant method is used to calculate the root of the function. The formula for the secant method…

Q: 2. Evaluate the integrals. (a) S (b) [9rc (c) J (d) O 1+ e²r 9x cot(x²)dx -do -dx cos sin² 0 +1 -dx…

A: As per the guidelines we can solve 3 parts only

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: Solve the solutions of (e + Iny +) dz + ( + + In r + siny) dy %3D

A: We will answer the first question as we don't answer multiple questions at a time. Please resubmit…

Q: A. y,(x) = Ax + Bx + C, B. y,(x)= Ae", C. yp(x) = A cos 2a +B sin 2x, D. yp(1) = (Ar + B) cos 2x +…

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Q: It can be shown that y, = ex sin(6x) and y2 = e'x cos(6x) are solutions to the differential equation…

A: Here we have been given the solutions to the differential equation  y1=e3xsin(6x)y2=e3xcos(6x)

Q: Find the solution of the heat conduction problem Uxx = 4u;, 0 0; и(0,г) — 0, u(2, t) = 0, t > 0;…

A: In this question we solve the heat equation and find the value of u(x,t) as t goes to infinity.

Q: Which of the following functions is a solution of dx 12x – 8y dt dy 16x – 4y dt O a. æ(t) = et…

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Q: Consider the IVP y'=sin° y +1 for y(0) = 0. (a) Use Euler's method to approximate the solution for…

A: Given the equation y'=sin3(y)+1, y(0)=0

Q: 2) Consider the DE: y" + 25y = 0 A) Verify that y = C₁ cos 5x + c₂ sin 5x is a solution of the given…

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Q: 14. A form of a particular solution for the DE (using undetermined coefficient method) + 3yl4 + 5v"…

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Q: What is the integral of f cos¹ (2t)dt? Ot+sin(4t) + sin(8t)] + C None of the choices cos" (2x)…

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Q: Which of the following is the correct form of the solution to the non- dy homogeneous equation for…

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

Q: 16. Solve the exact DE with initial cond'n x(0)=1: (3x – Siny+2y)dx+(2.x – xCosy+1)dy = 0 а. 4ху +…

A: We have to solve given exact differential equation.

Q: Which is an appropriate trial form for the non-homogeneous equation y/" + 2y' + 5y = e' cos(2t) (a)…

A: Given: y''+2y'+5y = etcos(2t) To write: Appropriate trial form for the given non - homogeneous…

Q: 15. Evaluate the given integral, V4 – 9x² dx: arc sin () A. x V4-9x2 2 arc sin () x V4–9x² В. + c 2…

A: Giiven: To evaluate the integral∫4-9x2 dxFormula: ∫a2-x2 dx=x2a2-x2+a22 sin-1xa+c

Q: 15. A form of a particular solution for the DE y(4) + 3y + 5y" = 72 using undetermined coefficient…

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Q: [D/HD] A different PDE has a full general solution is of the form which of the following is a…

A: Given is the initial condition u(x,0)=sin(6πx)+sin(15πx) The objective is to choose the possible…

Q: Evaluate the Integral dx – (**V2Tan-1x-(Tan-1x)2 1-х4 '2Tan-1x-(Тап-1x)2 3. S х?/2Tап-1x- (Тап-1x)2…

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Q: What is the general solution of the following ODE 2u sin(1) Hint: use integration factor method…

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Q: y" +Zy+3y=sin (3x)

A: Given that,  y''+2y'+3y=sin(3x) The auxiliary equation is m2+2m+3=0m=-2±4-122=-2±2i22=-1±i2…

Q: By direct partial integration, Solve the following PDES 8- 82u = COSX COSYSXUCX,t) Ex u(π, y) = 2…

A: Given ; del2u/delx del y=cosxcosy.

Q: 6. Find the general solution of (cos cos y +ycos x) dx+ (sin sin x – x sin sin y ) dy = 0 A. x cos y…

A: As per the guidelines I am supposed to do the first question among multiple questions. So I am…

Q: Find the solution of the heat conduction problem. 100uxx = ut,   0 0 u(0, t) = 0,   u(1, t) = 0,…

A: The solution of the heat problem is given by u(x,t)=∑k=1∞  aksinkπxle-α2π2k2tl2   where ak=2l∫0l…

Q: What is the general solution to the DE, !! dt 2? - 2x + 2? What is the general solution to th O In…

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Q: Evaluate the integrals: 1- dx TT/2 7cos t sin t dt 0. 2-

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Q: 3-Evaluate the integrals in Exercises: 2√3 So dx √4 + 4 + x² 0 4- 6 dx 5. Sot v Jo V1 + 9x² cos x dx…

A: We have to evaluate the integrals.

Q: I. Evaluate the following Definite Integral. 1.) L,9 6x3+4x2-8x dx 2.) x²(2x³ + 1) dx 2x 3.) sž…

A: Integration

Q: sin ® 3y cos3ydy cos 3y dy

A: We have to find out the integral

Q: Q1\ Differentiate the following (c 1)2xsin-13x 2)y = In *+1 Vx-2 %3D 3)y %3D sin-1 2x

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Q: 2х n evaluating J cos²(2x) Tx using integration by parts, identify the portion of the integrand to…

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Q: 25 2 8 5 cos (x²) 4Vz Evaluate the integral -dx dy dz by changing the order of integration in an…

A: Consider the provided question, We have to find the integral ∫025∫02∫4y85cosx24zdxdydz by changing…

Q: Evaluate using Integration by parts. J cos 2x sin 3x dx cos 2x cos 3x - sin 2x sin 3x + C None of…

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Q: 1. The solution to the non-homogeneous DE (D? + 2D +5) y = 3 e* sin x - 10 is a. e* cos x -2 + 8* (a…

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

Q: Evaluate the integrals et + 2e²' – e' dt e' dt 39. 40. e21 + 3e' + 2 e21 + 1 cos ydy sin? y + sin y…

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

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

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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: Find the differential dy: y = sin(av). dy = " cos (av) [2v + a+i In a (1 + Ina p + x!+ In ¤ (1+ ln…

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Q: Consider the D.E. y(4) + 4y" = 1 – cos(2æ). Then a suitable form of the particular solution can be…

A: Let us consider the  differential equation F(D) y=Q(x) then the particular solution is obtained by…

Q: Let u = cos(4x) and du = e² da, then by using IBP, the integral [e²= cos(4x) e2x cos(4x) dx is equal…

A: Given, u=cos4x and dv=e2xdx. Formula for IBP: ∫udv=uv-∫vdu

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.