Find the general solution of y) + 3y(4) +y"'' + 3y"= 0. A. y = C1 + C2t + C3 cost + C4 sint + Cse 3t B. y = c1 + C2t + C3 cos3t + C4 sin3t + Csert O C. y = C;ef + czt et + C3 cost + C4 sint + Cge-3t D. y = C1 + Czt + C3 cos3t + C4 sin3t + Cge3t E. y = c; + Czt + C3t² + C4 Cost + C5 sint

Q: Solve for x, y and z x + 2y - z = 0 2x + 3y - 2z = 3 -x - 4y + 3z = - 2

A: x+2y-z=0            i2x+3y-2y=3        ii-x-4y+3z=-2    iiii+iii-2y+2z=-2⇒-y+z=-1…

Q: Construct an equation whose roots are the reciprocal of the roots of 2x +4x -10x-5=0

A: Consider a cubic equation ax3+bx2+cx+d=0 where a≠0 and assuming α,β and γ are roots of equation then…

Q: 1) S dx 9-x2 dx 2) J2y-2 x2Vx2 -2 3) dx 2 V1-x2 |3D

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Q: Solve using MUC. y" +4y=3sin2x 3+3+5+ y = C₁ cos2x+ C₂sin2x - -Xcos2x 4 y=C₁ cos2x + C₂sin2x +…

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Q: (1+ ye" + xye")dæ + (xe² + 2)dy = 0 C = xye² + 2y+ x C = xye" – 2y – x %3D - Option 3 O Option 4 C =…

A: ANSWER: Option 3.

Q: Solve for u. u/2 + 3u/4 = u/8

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Q: a) x2y"+ xy' +(x2- 25)y = 0 b) (1 - x2) y" - 2xy' + 42y = 0 %3D %3D

A: a. Bessel ordinary differential equation has the form of x2y''+xy'+x2-v2y=0. Now, Rewriting the…

Q: What are the solutions of the equation 2sin(4x)=1 on the interval [0,n)?

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Q: В. NON-HOMOGENEOUS HIGHER ORDERED LDE 1. (D3 + 5D² + 3D - 9)y = 64x²e-3x 2. (D³ + 13D - 34)y = 25x2…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: When you plug in (0,0,0) into 7x - 5y + z = 0. It holds true, however, when you plug in (1,1,1) into…

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Q: Solve for x + y (EZ) if i) x² - y² = 24, ii) xy = 35

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Q: 5) Solve y) - 3y4+3y" - 3y" +2y' = 0.

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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: y/" – 4y" + 53y = 0 O y = C1 + C2e cos2x + C3e-7* sin2x 7x O y = C1 + C2e cos2x + C3 e7"…

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Q: Solve for x: xy2 + yz2 - 4 = 2x - 1. 3-yz2 b) х %3D у2-2 a) x = *y^tyz2-3 2 с) х %3D 3 — yz2 -у? +2…

A: Consider the given expression.

Q: dx 1-S 1-sinx

A: “Since you have posted multiple questions, we will solve first question for you. To get remaining…

Q: DETERMINE SOLUTION OF 1 x dy dx + y = x² + x (2x+3y-13) dx + 3x - 2y) dy = 0 DE

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Q: Solve: y" + 4y" + 29y' = 0 O y = C1 + C2e5ª cos2x + C3e5" sin2x -2а O y = C1 + C2e¬2ª cos5x + C3e¬2®…

A: The given equation is y'''+4y''+29y'=0 First write the auxiliary equation and then solve it to…

Q: Solve for the particular solution of the given IVP: O (t^2+y^2)^1.5 - 3ty = 89 O (t^2+y^2)^3 - 3ty =…

A: The given initial value problem is: dydt+y-tt2+y2t-yt2+y2=0 ;       y(4)=3

Q: 1 Q6 Solve y" + 3y + 2y = 1² 1+e

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Q: Ex. (9) Solve 3y"-2y' + y = 4x+2

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Q: 5) x2. dx = x² + 3xy + y², (c) dr = 2 = 3v, + 3x' (d) (1 - y)' + By - 5x = 0.

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Q: Find the general solution for y"" + 2y" + 2y' = 0

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Q: What is the special solution of the equation y0̅ ? y''' + 5y'' + 12y' + 8y =5sin2x +10x2 - 3x + 7

A: Find the attachment

Q: Select all equations that are equivalent to a-6z 16. a + 6x 9 0 O b a + 6x +9 = 16 Oc a+6x + 9 = 25…

A: Solution:-Given equation,     x2+6x=16  —1let us see and solve each option given,a…

Q: If u(x) = x3, then du = 3x2.

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Q: -y(2x+y) x(x+2y) - y'=-

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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: Differentiate. 1) f(x) = 4x2 - 5x+4 A) f'(x) = 4x-5 2) y = (2x² + 3x)² A) B) f'(x) = 4x²-5 = 8x3 +…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find a general solution of y"=(-2+2isqrt(3))y

A: Given that, the differential equation is- y''=-2+2i3y On simplifying, y''--2+2i3y=0

Q: The general solution to the ODE x²y" + 2xy' - 2y = 0 is y = C1x + C2x-2. Use variation of parameters…

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Q: x + 1) ² − 4(x + 1) dx + 4y = 0. Given that y₁ = ²x is a solution; find the general solution. dy dx²…

A: Solution to the differential equation

Q: Solve: y" + 9y = 9csc3x O y = C1 cos3x + C2 sin3x – 3xcos3x + sin3xln(sin3x)

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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.