Determine the form of a particular solution (u,) of the given DE u" + 6u' + 9u = (7t + 2t )e¯*. o 4, =t (At + Bt)e* -3t o4, =t (At + Bt +Ct + D)e* -3t o 4, =t°(At +Bt +Ct + D)e* o4, =t*(At' +Bt)e AMoving to another question will save this response.

Q: A) L{t//4} : (5/4)! a+5 B) L{u-2(t)} C) L{e"u(t)} 8- 5 3! D) L{t*e"} = E) e{icm (;)} 5Cos s(s – 2)…

A: A is false  B is false  C is true  D is false  E is false  The detailed solution is as follows…

Q: 2. у" - Зу' + 2y %3D е*

A: As per our guideline we are supposed to solve only one question

Q: Find the general solution to + 18y" + 81y = 243 + cos6t O y = c1cos18t + c2sin18t + t(c3 cos18t +…

A: The solution is given as

Q: 0'+ 374 3D+ 1)y -8sinx ylo): -/ 5- y"/6)=5

A:

Q: 4. A = [ 5 7 5 ²]. b = = ['₁ 5 12 17

A: Given,

Q: Example 7: Find the solution of y + 2ý + 4y =x cos 3x The chr. Eq. is r? + 2r + 4 = 0 -bt vb2 - 4ac…

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

Q: Find the general solution of the D.E. (y^2- 2xy + 6x) dx = (x^2 - 2xy + 2) dy = 0 Show your…

A:

Q: The solution of e^z=−3 has the form x+i(y+2nπ) where n is an integer. a)What is the value of x?…

A:

Q: Find y' where y = tan(11a? + 8) v173 + 17 Answer: 51a2 y/ = sec2 (22æ)\/172³ + 17+ tan(11a² + 8)…

A: I have used the rule for composition of function and multiplication of functions

Q: 3y2+8zy y' = 4x2+2zy denkleminin genel ҫӧzй О а. х^(2)+4ху-су О b. 4y^(2)+ху-сх О с. 4у^…

A:

Q: Euder-Caue

A:

Q: Find the general solution of i = Ax, where A = .

A:

Q: 2y" + 3y' - 2y = 3xez* - 2sinnx (Use Method of Undetermined Coefficients (MUC))

A: The given differential equation 2y''+3y'-2y=3xe12x-2sinπx. We have to find the general solution…

Q: 2. Solve the initial value problem z""+x" - 4x' - 4x = 0, x(0) = 1, x'(0) = 0, x" (0) = -1. Hint:…

A:

Q: The nonhomogeneous equation with constant coefficients such that the general solution is…

A:

Q: The solution of the following Bernoulli's equation y' + 3x²y = 4x²y² is: Oy= 3/(4+3Ce^(x^3 ) ) Oy=…

A: The given Bernoulli's equation is, y'+3x2y=4x2y2. To find: The solution of the given differential…

Q: Give the general solution to xу +5ху%3D х 3 sin(4x). a) Oy = x cos(4x) + Cx-5 b) Oy = -* cos(4x) +…

A:

Q: 4) L-¹{₂}=L-¹ { } } * L-¹{₂} 31 pt 2-t-

A:

Q: Find the general solution of ху — у 3D 2x In(х). а) Оу%3D х In(x) + Сх b) Oy = x(In(x))² + Cx с) Оу…

A:

Q: Find all real singular points of x(x2 –7 x + 10) y" + sin(x) y' +x y =0. {-6, –6} None {5, 2} {4, 3}…

A:

Q: If w = 1/r and r^2 = x^2 + y^2 + z^2 , then what is the value of xwz + ywy + zwz -1/r^2 O -1/r 1/r^2…

A:

Q: y"+y' + (a) -5 x-b = 0, Xo = 2 is 5. (b)-3 (c)-2 d)-8 Q7) L(y") = a) s²L(y(x)) + sy(0) - y'(0) c)…

A: We have given the answer in the next step. Hope you understand that

Q: 4. Find the general solution to the DE 2x²y + xy'-3y=0.given that y₁=- is solution.

A:

Q: 9. Find the general solution of (D² – 2D+ 1)y= 6e*. A) y= (c, +c,x)e* + 3e™* B) y= (c, +c,x+ 3x² )e*…

A:

Q: 3) L-1{}.} } = L {{}L'{}

A: Please see the attachment

Q: 3-VE For dz, z = 2+vz

A: Given,             ∫3-z2+zdz

Q: Find the general solution of у "— 2у "— 16у'+ 32у -0 given that r = 2 is a root of the…

A:

Q: 2. Let AX = B with 2 1 1 3 ^= [₁ ²²² =²×²0 EJ A: 0 -3 -2 B X y ) 2 1 use the fact that 1 A-¹ = 2 -3…

A: We have to find the value of variable and verify them the result

Q: Solve the IVP: X' = AX, where -() xw - () 3 -3 1 A = 2 -1 0 1 -1 1 and 7 X(0) 4 3

A:

Q: Əz x²y + 7y²z + xz² = 9 ax'

A:

Q: 2. y' -5y "t 4y'=6 yo). "() = 47 sol'u y"()=" y "C0)=23

A: We have to solve the given problem.

Q: Find the most suitable form for a particular solution ay of y" +9y=-4est+tsin (34) in the method of…

A: Here, we have to find the most general form of particular solution of given differential equation by…

Q: Solve for the general solution xydx - (x² +2y² ) dy = 0 x² = 4y° In(2 ) xy = 4y° In() Option 1…

A:

Q: Solve z? – 2z+4 = 0. Let u and v be the solutions of z? – 2z +4 = 0, then: A. u = -1 – iv3 and v =…

A:

Q: Verify that y = c1x+c2Vx+ is the general solution of the 6x following nonhomogeneous 2.²y" – xy' + y…

A: Derivative of xn: Derivative of an exponential function that is, xn is given by the formula,…

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.