Obtain the general solution unless otherwise instructed LINEAR EQUATIONS WITH CONSTANT COEFFICIENTS a.) (D3 − 4D2 + 4D)y = 0 b.) (2D4 − 3D3 − 2D2)y = 0 c.) (D5 − 16D3)y = 0   this is the example of answer format: y = C1cos x + C2 sin x +C3cos 2x + C4 sin 2x

Q: Solve the given DE using 3 possible solutions: y' X 3 - 2y 3 3xy 2

A: Given DE  y'=x3-2y33xy2  …………………………(i) we can write it as dydx=x3-2y33xy2

Q: y(6) – 4y(5) +3y/9) =-27 %3D

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Q: Solve the Cauchy euler equation d³y x3 dx3 3x2 d?y dx2 2 + 6x -6y = 3 + Inx³ dy dx

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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: A. Find the family of solutions of the following equation using linear differentic equations. 1. y'…

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Q: (x² + 4xy + 2y²)dy + xydx = 0

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Q: Find the general solution of (D4+ 50D²+625) y=0_ A y=c,cos5x +c,sin5x ® y=c,e*+c,x* +cze-5«.…

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Q: Determine the values of the variables to satisfy the equation using a) Jacobi and b) Gauss-Seidel.…

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

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Q: b) Using Gauss Jordan, solve the following equations. 5x + 2y =2 2x + y - z =0 2x + 3y – z =3

A: Total Equations are 35x+2y+0z=1→(1)2x+y-z=0→(2)2x+3y-z=3→(3)Converting given equations into matrix…

Q: dx -2xcsc 2y – 2x³cos 2y dy sec 2y

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Q: Which of the following equations is/are exact? b 32 ydx + (2a'y+ 4y) dy = 0 %3D O (ry + 1) dr + (ry-…

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Q: Exercise: Apply V=mu and then (*y)=fcx)+ JCY) to solve the fellowing equation 2. 11

A: Given equation is, x2ux2+y2uy2=xyu2.....(1) And,  v=lnu....2vx,y=fx+gy.....3 Aolving equation (2) we…

Q: The Cauchy-Euler equation can be reduced to an equation with constant coefficients by means of the…

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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: (b) Solve given BVP by using collocation method. u" + 2u' 6t 0<t<1 with u(0) = 0, u(1) = 1

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Q: The general solution of (D²+2D +1)(D²+4)y=0 is A y=(C,+Cx)e+C,cos2r + C ,sin2r B…

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Q: Find the solution. (D4+2D³ + 10D²)y =0. y = c,+c,x+e¯*(c,cos3x +c,sin3x) C B y = (c,+c,)x+e-(c,cos3x…

A: Given Differential equation is D2+2D3+10D2y = 0

Q: B. Prove that the given equation is a solution to the given DE: 1. = C,e3* + Cze2* + Cze* ; y"- 6y"…

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Q: Q2) Solve the following equation Cauchy Euler Equation Method 2a?b" + 3ab' – 15b = 0 where, b(1) = 0…

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Q: Find the general solution of dfferential equation (D² -6D +8)y -2x e t Sin 5X

A: This question belongs to the differential equations and we have to calculate the general solution of…

Q: 1. (3x – 2y + 1) dx + (3x- 2y +3) dy = 0, %3D Ans. 5(x + y+ c) = 2 In | 15x - 10y + 11L

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Q: Which of the following equations is the DE whose solution correspond to y = C1sin3x + C2cos3x + 9x²…

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Q: 2y Solve the I.V.P y'+ =1-, y(0) = yo, then find the value 2 3 of for which the solution touches ,…

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

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Q: Find the solution. (D4 + 18D2 + 81)y = 0 A y = (c, + c,x)e²"cos3x + (c,+cx)e2'sin3x. y = (c, + c,)…

A: 16 Given differential equation is D4+18D2+81y=0 We have to find the general solution of the given…

Q: Show that the equation Əy 2 a3y + 2k possesses solutions of the form 00 -kt E C,e cos (C, x+ E,) cos…

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Q: The general solution of (D²+2D+1)(D²+4)y=0 @ -+Ceª A y=(C,+Cx)e*+C;e B none of the given choices ©…

A: We have to find out the solutions

Q: (D² – 3D + 2)y = e2×(1 + e2x)¯ -

A: Given: D2-3D+2y=e2x(1+e2x)-1 Formula used:y=yh+yp

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: Which of the following is solution of (D3+2D2+D)y=0(D3+2D2+D)y=0 ? a.…

A: We have given  differential equation D3+2D2+Dy=0 Auxiliary equation of diferential equation…

Q: 9. Find the general Solution of the following DE. a. (D - 4D2+ 4D)y = 0. b. (9D + 6D² + D)y = 0. c.…

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Q: Use the method of Frobenius to solve the given equations. a) 2x?y" – xy' + (x² + 1)y = 0 b) 2x?y" +…

A: Since the solutions of the given equations are very lengthy in Frobenius Method , i gave the…

Q: Determine three linearly independent solutions to the equation y" + 2y" – 3y = 0 of the form y(x) =…

A: The given differential equation is                                                y'''+2y''-3y'=0

Q: 8. Solve the system of equations using Cramer's Rule. 12x - 11y = 140 7x +9y = 20 |Dyl y%3= |D| |Dx|…

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Q: Using the method of variation of parameters, the form of a particular solution Yp of (D²+25)y=4x²…

A: First we need to check complementary solution  So, consider homogeneous equation÷ D2+25=0 Auxiliary…

Q: A. If:Z = x + iy, Solve the following equation to find x and y: 4x+ y_ 4y+14 -0 then use Demoivre's…

A: Given: - If Z=x+iy and the equation is, 4x+y1+ix-4y+i4iy=0 To find: -The value of x and y. Then use…

Q: Apply the method of undetermined coefficients to find a particular solution to the following system.…

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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: If y(t) is the solution of - 2y = 4, y(0) =1, then y(t)= %3D %3D

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Q: How many solutions are there between planes P₁: 2xy + 2z = 2 and P₂: -x + 2y + z = 1? If there…

A: Given is the equation of two planes. The objective is to find the number of solutions between the…

Q: The equation dy/dx = A(x)y² + B(x)y + C(x) is called a Riccati equation. Suppose that one particular…

A: Differentiate the equation of y with respect to x.

Q: HW-1- 2dn Course Using the method of separation of variables, find the solution of the following…

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Q: dy. Find the particular solution: t 2y 2t, y(-2) = 4 %3D %3D

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Q: Determine the values of the variables to satisfy the equation using a) Jacobi and b) Gauss-Seidel.…

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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: c) Using the results in a) and b), give a particular solution for y" – 2y' + y = 3e* + 1+x2

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Q: E Solve the defferential equation 71 Jy 27 dy COSX 31xdy-y= x²_ y² 2. xP

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