The particular solution for the equation, D2(D+2)(D2+1)2y=e-2x, is in the form of yp=?e-2x. a) A b) Ax2 c) Asin(x) d) Acos(x) e) Ax

Q: Exercises: 1. Show that y=3e*-e* is a solution to y"-4y=0

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Q: The equation z* + 4 = 0 has no solution. %3D Select one: O True False

A: We have to check the given equation has solution or not

Q: When solving Jx² + 4y? = 16 Lx² - y? = 1 %3D by the addition method, we obtain y² = 3, so the…

A: Given that, x2+4y2=16x2-y2=1 And solution is y2=3

Q: y(6) – 4y(5) +3y/9) =-27 %3D

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Q: Find c such that the equations below have no solutions. x + 2y = 1 cx + 10y = 4 Then c =

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Q: (D5 -D* – 2D³ +18D² –31D+15)y =0

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Q: solve the DE y'' - 5y' + 6y = 32xe2x, y(0) = 1, y'(0) = 0

A: *Concept:- the give differential equation is Linear differential equation of higher order with…

Q: y = x + C,e* + C,e-2*

A: y=x+C1ex+C2e-2x

Q: (c) Zo= 2.15 (d) Zo = 1.95 (e) Zo= -0.35

A: The test is right tailed.

Q: ?The Third Equation for i3 7in+12i3-=-3-O 5i1+12i3=0- Zir-4i2+16i3=-3- 0

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Q: We are also given that eRd, where is that in the solution?

A: The previous answer is not correct....See this answer

Q: B. Prove that the given equation is a solution to the given DE: 1. = C,e3* + C2e²* + C3e* ; y"" –…

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Q: Verify that y, = e2x and y2 = e5×are solutions of у" - 7у' + 10у %3D 0

A: We have to verify that the functions y1=e2x and y2=e5x are solutions to the given differential…

Q: If x, y belongs to Z prove that the equation x^2+4x-8y=11 has no solution

A: The given equation is, -----(1)

Q: Solve numerically Au = 0, u(0, y) = 70, u(3, y) = 0, u(х, 0) 3D 10, и(х, 3) —D 90, 0<х <3 0 < x <…

A: Given that: ∆u=0,…

Q: 2²y" - 4.xy+6y= 0, y(2)=0, y'(2) = 4 %3D

A: The differential equation is given as x2y''-4xy'+6y=0x2D2y-4xDy+6y=0x2D2-4xD+6y=0 It is a Cauchy…

Q: Solve by VP: y"' – 3y" + 2y' - et 1+e-x

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Q: 2. Verify that e 2 is a solution of the equation y" -3y'+2y=0.

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Q: • Jeze 39. et dt e²t + 3e¹ + 2

A: Given integral is I=∫etdte2t+3et+2 To evaluate the integral.

Q: 2 11 3. x*y" – 5xy'+9y= 2x

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Q: The solution of the IVP, y' = -2xy, y(0) = 2, is: %3D

A:

Q: Find the solution for the equations using Gauss-Jordan. Then ONLY give the answer for x+ y+x…

A: Given: x+y+2z=92x+4y−3z=13x+6y−5z=0

Q: 2a) find a solution of y" (x) = y(x) that passes the origin and go trhout the point (In(2),-).

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Q: Find the solution, (D3+3D2+3D+1)y = 0 A y = c,e*+ (c,x+czx²)e-* y = c,+c,e"+c;e¯ B C D y =…

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Q: b) Find particular solution of х*у %3D- (х* - 1) у, У(1) %3D 1.

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Q: Using a suitable substitution, solve z* + 3z2 – 28 = 0, qu x lo 219wog - (ahem A) where z E C

A: Given equation is        z4+3z2-28=0 , z∈ℂ We will solve this equation by suitable substitution.

Q: (a) Solve the following linear equation by Cramar's rule:- x- y + 2z = –-4 3x + y – 4z = -6 2x + 3y…

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Q: Observe that y = x is a particular solution of the equation %3D 2x²y" + xy' – y = 0 and find the…

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Q: Solve the IVP given below y" +4 y' +4 y=0, y(0) = 0, y'(0) = – 3.

A: Given y"+4y'+4y=0 ,y(0)=0 and y'(0)=-3

Q: If e-x, xe-x are the solutions of y''+ay'+by=0 then, what are the values of a and b.

A: To find- If e-x, xe-x are the solutions of y'' + ay' + by = 0 then, what are the values of a and b.

Q: There is a solution z e C to the equation + 2 = 0. Select one: OTrue OFalse

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Q: — хz + 2ху %3 0. xy ay az az Solve, y? ax

A: Lagrange's Method: Let us consider a standard form of the first order partial differential equation…

Q: An Euler-Cauchy equation is given as x*y" +1.5xy – 0.5y=0, x(1)=5, 19 (9). 3 Solve the equation by…

A: Here, we have given that the Euler-Cauchy equation x2y''+1.5xy'-0.5y=0 and the initial conditions…

Q: (a) Solve the following linear equation by Cramar's rule:- x - y + 2z = -4 3x + y - 4z = -6 2х +…

A: We have given equation x-y+2z=-4 3x+y-4z =-6 2x+3y-4z=4 Matrix representation of equation  AX=B…

Q: Use Gaussian Eleminetion to solve 20+ y + 2Z =8 3y + 3Z a-4 4¢ + 24 - Z = Iv

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Q: a) Solve the following linear equation by Cramar's rule:- - y+ 2z = -4 x + y - 4z =-6 x+ 3y – 4z = 4

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

Q: Question 1 Explain that (AB)" = BT AT 21 A = 0 1 3 402 1 and B = 2 0 -1 1 1 -2 1 3

A: Let's find.

Q: The roots of the auxiliary equation of a DE are: m 3, 3, 3 t 3i.Then solution of the equation is,

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Q: X-+ Solve y(x) = Fow + by First Finding Kalkit l,FX,t, A) and Solution when FW=e2X FN = e=X

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Q: : Ebobl Qf solve the initiat Valu problem %3esince-2) y(an2) =a

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Q: ,2 y² e2y dy = e2y 2 (y² y + C 4 2

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Q: Find Solution AUP : gruen xlo)=2 4 %3D - -3

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Q: - 9y" = 27 %3D

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Q: Show that the equation e^x = 1 − x has exactly one solution in R. Find this solution

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Q: solve fos given, dy 2. -2t "ट +-

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Q: A fundamental solution set for the D.E. y(4) – y" – 12y = 0 %3D

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Q: 3x?y" + 2xy' = 05 21"

A: Differential equation

Q: 'ind the general solution of d³y 6. dr3 dy - 8y = 21e2 dr dr2

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Q: If e-x, xe-x are the solutions of y''+ay'+by=0 then, y=cx/ex is also a solution of y''+ay'+by=0.…

A: Let us consider the given differential equation y''+py'+qy=0 To solve the differential equation…

Q: The solution of the IVP y" + 9y=0, y(0) = 1, y'(o) = 0, is %3D

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.