(D4 + 3D3 – 6D² – 28D – 24)y = 0 (D3 + 3D2 + 3D + 2)y = 0 -

Q: Vy - y 3 b) dy 2 y²

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Q: (D³ – 4D²D'+ 5DD² – 2D ) z = e'*2* + Vy +x.

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Q: 2) (D² + 2D + 1) y = [exp(x) - 1]-2 %3D

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Q: D'y- 4. (4D - 4D³ - 23D2 + 12D +36)y = 0 5. (D° + 3D² + 3D + 2)y = 0 Dy +y = 0

A: The given differential equation is: (4D4-4D3-23D2+12D+36)y=0 The auxiliary equation is:…

Q: dy Find if y 3e2 3z 一山 %3D O -9e 2

A: Using chain rule of differentiation.

Q: (D³ + 4D² + 9D + 10)y - 24 e*; when x = 0, y = 0, y' = -4, y" = 10. %3D

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Q: Non Homogeneous: (D2 − 7D + 6)y = 3x2 − 2x + 5

A: Here we have to solve the non-homogeneous differential equations     (D2-7D+6)y = 3x2 - 2x +5 .

Q: 5. (D³2D+4)y=0; y = -2, Dy = 8, D²y = 0, when x = 0.

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Q: 1. (D³ + 3D² - 4D - 12)y = 0 2. - d'x 19+ 30 = 0 dt3 dt 3. (4D4 - 8D³ - 7D² + 11D + 6)y = 0

A: 1). From the given differential equation; D3+3D2-4D-12y=0 So, The auxiliary equation is:…

Q: %3D 0 аnd y' ) = vz 2. у(x) %3D Сisin2x + Czcos2x + 1; C1 = C2

A: Given  y(x) = C1sin2x+C2cos2x+1 On applying the initial condition yπ8 = 0 , we get yπ8 =…

Q: (D4 + 3D3 – 6D² – 28D – 24)y = 0 A. y = c;e2x + C2xe2x + C3e-3* + C4xe + C4xe-3x B. y = ce2* + c2e"…

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Q: Eo f is y = 1(a- 4). 3D1

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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: (4x-3) find dy/dх y = (2х-7)6

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Q: (D³– 4D°D'+ 5DD2 – 2D ) z = e'*2* + Vy + +2x +Vy +x. |

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Q: 19. (D2 + 2D – 4)y = 32 %3D a. y = C1e(-1+v5x) + C2e(-1-v5x) + 8 b.y = C1e(-1+v5x) + Czol-5x) –8 c.y…

A: Let's find.

Q: 2. x3 - y3 = c³, find y" %3D HOOAT d²x 3. x* = at?, find dt2 1983

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Q: B. Non- homogeneous Higher Ordered LDE 2 1.D +50² + 8D -9) y - 69x²e-*

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Q: how can i find the vectorial equation for d1:3x/2=y-1 and d2:?x+y-6=0

A: Given: vector equation for  L1:   3x/2=y-1 l2  :   x+y-6=0

Q: 3. (D2 + 2D + 1)y = 0; when x = 0, y = 1, Dy = - 1.

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Q: Find dy/d 5x²+xy+ N9 - Say %3D =D0

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Q: (3x*-5)(2x +9x-6 of y= dy and %3D Determine the 7x

A: Simplify the equation. y=6x7-10x3+27x5-45x-18x4+307x5=67x2-107·1x2+277-457·1x4-187·1x+307·1x5

Q: Q3:A/ Find: dy dy y 2 Vy (1 + Vý)² yV4y? – 1 |

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Q: in yy = 2 y-x; %3D

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Q: dz If x4 – y4 + z - 3z = 2, then %3D %D dx a) 4x3-4y3 3-4z3 b) 4x3 3-4z3 c) None of these d) 4x3+4z3…

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Q: P (Likes spicy food | Masters) = %3D D. P (Masters | Likes spicy food) = %3D F. P (Juniors and Does…

A: Conditional Probability

Q: 2. (D² + 3D + 2)y= 1+ 3x + x²

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Q: + 12D + 36)y = 0 5. (D³ + 3D² + 3D + 6 (D3 AD3

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Q: 3. D'y - D'y- Dy + y = 0 (AD4

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Q: f(x) = (4e2x)3 3(4e2*)2(4e2x) 3D3(16e**)(4e2*) 192(e6x) %3D %3D %3D

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Q: z = 2 24 z=Vx² + y² 2 FIGURE 9

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Q: (D³ + 7D² + 19D + 13)y = 0 when x = 0,y = 0,y' = 2,y" = -12 %3D %3D

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Q: Qs) y" + 3y' + 2y = e* – 3

A: See the details solution in below

Q: (D² – 3D – 4)y = 0 is ° y = C,e** + C,e* " y = C,e** + C,e* 4х 4x -X -4x ° y = C,e** + C,e* y = C,e*…

A:

Q: (D³ – D)y = 4e * + 3e2x X. a. Ур а. у, — 2хе * + 2xe+ +-e e2x b. Yp = 2xe +e2* X- 3 2x C. Yp = 3xe 2…

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Q: 4. (D3 – 4D² + 4D)y = 0 5. (2D4 – 3D3 – 2D²)y = 0 - -

A: (4). The given differential equation is: D3-4D2+4Dy=0 So, the auxiliary equation is: m3-4m2+4m=0

Q: 3x+2y=D-14 x-Dy-3

A: the given system3x+2y=-14x=y-3we have to solve the system by the substitution method.

Q: d³r dz +t- dt3 (c) 4tx = 0 %3D dt

A: The solution is given as

Q: Solve the dff oq dy 3x寸票-5-2 %3D

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Q: (D + 3D + 2)y = xsin 2x

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Q: 4. (Dª + 2D³ – 6D² – 16D – 8)y = 0 - - - %3D

A: The given differential equation,     D4+2D3-6D2-16D-8y=0

Q: 3 1 (x + 2y)dydx -1 a) 5 b)7 O d)-:

A: Please check step 2 for solution.

Q: What is the discriminant of the PDE?    4d2/dy2=-3du/dx-4u

A: the discriminant of the PDE is :

Q: (D4 + 10D3 – 7D² – 76D – 60)y = 0 - -3x A. y = ce-2x + c2e¬3* + c3e2x + c3e¬5x B. y = ce=* + C2e¬4*…

A: Given differential equation,D4+10D3-7D2-76D-60y=0

Q: (D4 – 2D3 + 5D² – 8D + 4)y = 0 (D3 – D² + D – 1)y = 0 (4D3 + 12D2 + 13D + 10)y = 0 (D5 + D4 – 7D3 –…

A: Given

Q: 23D + 12D + 36) 5. (D + 3D² + 3D + 2)y = 0 6. (D3-4D2 + 7D)y = 0 7. (D + D)y = 0 %3D

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Q: What is the y=x excos 2x? (A (B) (D²+5)² C D²+5 D (D²-2D+5)² D²-2D+5 annihilator for G

A: Solution

Q: D’(D² – 4)y = 3x+ 2e¬3* | y = 3x + 2e¬3x m° – 5 - 4m³ = 0 ® m' (m2 – 4) = 3x+2e-3* D (D² - 4) = 0 3…

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Q: Q3) Find fog(x), gof(x), D, D fog' gof x+2e f(x) = » g(x) = vx – 2 %3D 2

A: Solution:-

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.