C. Find for the general solution of the following DE. 8. (D3 + 3D2 – 4D)y = 0 9. (DA + 6D3 + 9D²)y = 0 10. (Dª + 2D³ + 1OD²)y = 0 %3D

Q: Find the solution of the following IVP: y(t) = dy -2ty=9t²e², y(0) = 5. dt

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Q: 4. Verify if the following equations general solution: are exact and find the 2 9. 2xydx + (1 + x²)…

A:

Q: xarctanydx + dy = 0 2(1+ y²)

A:

Q: nd the general solution of the following: 2. (D3 – 4D² + 4D)y = 0 3. (4D2 – 6D + 1)y = 0 4. (25D2 –…

A: Topic:- differential equations  Note:- as per our guideline if more than one question uploaded than…

Q: II. Determine the solutions of the following DE. 1. (х — Зу + 2)dх + 3(х+ 3у — 4)dy %3D 0 2. (х — 4у…

A: (1).    The given differential equation is: (x-3y+2)dx+(3x+9y-12)dy=0

Q: 4y" – 4y' +y = 0; when x = 0, y = -2,y' = 2. %3D %3D %3|

A: Consider the provided question, 4y''-4y'+y=o;  when x=0, y=-2, y'=2  First write the auxiliary…

Q: Q2 Find the general solution of y" + 5y' +6y = 4e +5sin .x.

A:

Q: 4. For the DE y"-3y' x+3e", write the solution of the homogenous equation y., then write a…

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

Q: Use undetermined coefficients to find the particular solution to y'' + 7y' + 12y = 2e¯ Y,(t) =| 2e-t

A:

Q: Q5: Find the solution of the following D.Es: 1- x + 5y = x7 at x = +5y 2- y" + 4y + 2y = 13e³x 2, y…

A:

Q: Use undetermined coefficients to find the particular solution to y''+ 8y' + 15Y = e 2"(13 + 12x) (13…

A: Consider y''+8y'+15y=e-2x(13+12x) To find the particular solution using method of undetermined…

Q: Find the solution for the given DE. y +4y e", y (0) = 2 %3D y = -te" + 2e y = te+re y = te" + 2ee y…

A:

Q: 2. Use the mothed of variation of parameters to find the general solution of the following…

A: We can solve this using variation of parameters for three variables

Q: Solve the following DE's a) y" +y = 0 c) y"-4y' + 49y = 0 y(0) = 0, y' (0) = 5 b) y"" – 2y" + 4y' –…

A:

Q: Solve for the general solution : xydx – (x² + 2y²)dy = 0 Select the correct response: 2*y = 4y°…

A: The given differential equation is: xy dx-x2+2y2 dy=0

Q: Q2\ Find the general solution to the given Euler x?y – 3xy' + 9y = 0

A:

Q: Q1.Find the general solution of following PDE equation (a) (5z+ R)uz + (7x+ R)u, R (b) (z + R)u, +…

A:

Q: B. Find the general solution of each of the following Higher Order LDE with cc (Dª – 4D3 + 14D² -…

A:

Q: Consider the following IVP: y"+a?y = 0; y(0) = 1, y'(0) = 0 Find the general solution.

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Q: M = Find the solution to MCt,o)=m(t,1)= 0 nco,x) = x (1-x) 2.

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Q: 23. y²dx + (xy – 1)dy = 0

A: Let's find.

Q: Consider the following IVP: y"-3y'+2y = e3t; y(0) = 0, y'(0) = 0 Find the general solution. A y(t) e…

A: Given differential equation is y'' - 3y' + 2y = e3t ; y(0) = 0, y'(0) = 0

Q: 3. Solve the DE ty' + 2y = ont, 4. Solve dy dr 1+ y?

A:

Q: I. Obtain the general solution of the following: a) (D2 + 3D + 2)y = 1 + 3x + x2 b.) (D2 − 6D +…

A: Use rules of differential equations

Q: Q2. If the solution of the below first order D.E is y = C el(x.y) (x³ + xy²)y = y³ Find the f(x, y).

A:

Q: dy dr +y- y²e* 4. Find the general solution of a.ye*(C + x) = 1 b. ye* (С — х) %3 -1 с. уе* (С — х)…

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Q: Find solutions of the following equations by the method of separation of variables: 4. 2+= 0 at xe,…

A: 5.

Q: Consider the following IVP: y"+a2y = 0; y(0) = 1, y'(0) = 0   Find the general solution

A:

Q: Consider the following IVP: y"-3y'+2y = e3t; y(0) = 0, y'(0) = 0 Find the general solution. – 2e -2…

A:

Q: Q(4) Find the general solution of dy =(r- y+ 5). dr

A:

Q: 1. Find the solution of y" – 4y = 147 et %3D with y(0) = 1 and y' (0) = 9. %3D y =

A: The given equation is y” – 4y = 147 e5t. The given initial conditions are y(0) = 1 and y’(0) = 9.…

Q: Solve the following equation for c: 1 2-c-z 2-²-y 1 dz dy da 10

A:

Q: For the DE (D^4 + 3D^3 + 2D^2)y = 0, Find the value of y when x =1, for the particular solution that…

A:

Q: 7. Find the general solution of the following DE. a. (D2 – D- 2)y = 0. b. (D2 + 3D)y = 0. c. (D? – D…

A:

Q: What is the particular solution of rydx (r +2) dy = 0 when 0 and y 1? 4y(x + 2) e = y (x + 2) %3D 4a…

A: topic - differential equations last option is correct

Q: Obtain the general solution of the following: A. (D2 − 1)y = ex + 1 B. (D2 + 1)y = sec3x

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Q: Which of the following is the general solution to the equation (2x+9)y" +(2x+7)y-2Y3D0? O a. y=c_1…

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Q: dz (D² + 16)³(D² + 4D – 5)²(D² + 2D – 3)4z = 0, Dz = dx

A:

Q: solve the following D.E ,t<3 y" – 3y - 4y =- , y(0) = 0, y'(0) = 0 : ,t23

A: Here we will use Laplace transform method to solve the given differential equation.

Q: Q1: Find the general solution of the following first order D.Es? (Answer two only) CELE MAI ) c)…

A:

Q: Q(2) Find the general solution of (2r2 + y)dr + (x2y-r)dy 0.

A: Solve the differential equations using exact differential equation method

Q: Which of the following is not a solution to d'y dr? 4y +1 -2z O y = e2 + e O y = e2 . -2x e - 1 O y=…

A: we have to solve

Q: Q(5) Find the general solution of (r+2y- 4)dr - (2r +y- 5)dy = 0.

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Q: Find a particular solution to y" + 16y = 24 sec(4t). Yp |

A:

Q: Find the general equation of the following DE: 4. (D3 − D2 + D − 1)y = 4sinx

A: Given: (D3 − D2 + D − 1)y = 4sinx

Q: Find the solution of the following IVP: y(t) = = dy dt 2ty=9t²e, y(0) = 5.

A: We have to solve the given IVP.

Q: Find two values of n such that y = enI is a solution of y" + y' – 72y = 0

A: Given differential equation,  y'' + y' -72y = 0 To find the solution of above equation in form of…

Q: Find the particular solution to y" + 14y' + 49y = 0 which satisfies the initial conditions y(0) = 2…

A:

Q: 3. Find a second solution to y" – 25y = 0, given one solution y1(x) = e5z. %3D %3D

A: Given differential equation is y''-25y=0 &amp; y1x=e5x be one solution of the differential equation.…

Q: Use the method of reduction of order to find a second solution to t'y" + 2ty' – 2y = 0, t>0 Given y1…

A: