(D² - 4D + 5)y = e¯*; yp a. Yp 10 b. y, =#e* 10 C. y, =e* 10 d. y, =e* 10

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

A: 2) (D3+3D2+3D+2)y=0 The auxiliary equation is…

Q: 8- (y – y) dy

A:

Q: F(s) = (8s + 11)/[(s-4)(s²+9)] %3D

A:

Q: Find high order DE 6. (D4-5D² - 36)y = 0

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Q: d²y Find if 2x'-3y=7 dx²

A: Given that       2x3 - 3y2 = 7 Here we have to find     d2y/dx2

Q: dzy 5. If y = 4x3 + 3cosx + x2sinx + then find dx2

A: Formula of derivativ y'=dy/dx and d²y/dx² = y"

Q: d (7) Vtan²s+ 21 dt = dx

A: Explanation of the answer is as follows

Q: Find the general cowtion of the die. y9) + ya) - 24 =-e (9+67x+17 x²) + (861nax - o cosex) „(2).…

A: The given differential equation is , y(3)+y(2)-2y = -e3x(9+67x+17x2) +…

Q: b) - 2y dy

A: Integrate the following.      ∫y4-2y-4y-2dy

Q: (2siny + 1) = 4 and y(0) = what is x when y =n?

A:

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

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

A:

Q: 9-y" - 2y +2y=e; y(0) = 0, y(0) = 1

A:

Q: What is the relationship between 2.AXY and YXB?

A: Consider the figures,

Q: r/64–x² r61-x²-y² x dz dy dx -67+x²+y²

A:

Q: Ax) dx Mx) dr 16. 17. 18. -6 -6

A:

Q: V1-y² -1 0 kpxpzp (,x + zA),I „«-,S

A: The given integral is: I=∫-11∫01-y2∫0x y2+x2 dz dx dy

Q: let x= et then by the chain rule d3x/dx3 equals

A:

Q: d2y Find anž if 2x²-3y²=7 dx2

A: Given that 2x^3-3y^2=7

Q: @3Dy+12 D3=24

A:

Q: So* - y-³) dy 2.

A:

Q: a z = 4x³-6x²y²-y com x= 2sen(t) y=-3cos(t) e

A: #As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: Find y, of+ 3+2y 14x2 + 42x + 6 d'y dx a.) y, = 7x2-4 b.) y, = 7x2 + x-5 c.) yp 7x2-x- 3 d.) y, =…

A:

Q: 2 Find dyif y.+3x-7 and x =, 2t +1

A: As per our guidelines we are supposed to answer only one question.Since you have asked multiple…

Q: d3y find 3 5) If y = 4x + z %3D dx3

A: Given that: y=4x3+3x2

Q: d) S t3 – 2t2 – 1 dt t2

A: (d) We need to evaluate the following integral ∫13t3-2t2-1t2dt

Q: GiNen Y+ 3y -22 こ4 what is the value of - - マ+ メと 2y +3z = -1 X +y tz?

A:

Q: 2 a) y = Find y'. 3e (ax-5)4

A: Explanation and solutions is given below.....

Q: Which of the following gives the domain of

A: We have  fx=x9-x2   Domain: Domain is the set of all inputs for which the function is defined.…

Q: Find d2y/dx2 implicitly in terms of x and y.    x2 + y2 = 4

A:

Q: Solve using D-Operator 3. y + 2y + y = x²

A:

Q: 4. y=6-ax-x", y = x+l6, about the a %3D | yaxis

A:

Q: (D3 – 3D2 + 9D + 13)y = 0 sle plel Ja

A: The given differential equation is ;                    D3-3D2+9D+13y = 0 We have to find the…

Q: Find d3y dx3 of y = x³e-x

A:

Q: 5. (D5-11D4+19D³ + 115D² - 200D - 500)y = 0 Ans: y = C₂e-2x + C₂xe-2x + C₂e³x + C₂xe³x + С5x²e³x

A: To Solve: Solution of ODE

Q: 5. (D2 – 5D + 6)y = 18x2 + 12e2* (Assume yp = Ax² + Bx + C + Ee2x)

A:

Q: Qs) y" + 3y' + 2y = e* – 3

A: See the details solution in below

Q: Evaluate d2y/dx2 at the point (0, -9). x = t3 - 3t y = 3t2 - 9

A: Given: x = t3 - 3t y = 3t2 - 9

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: 3/2 y 3. dydx 3 X

A: A detailed solution is given below

Q: 11. Perpendicular to 5y = 2x – 6 and passes through the point (-1, 5)

A: topic - equation of a line perpendicular to given line

Q: dx What is the best substitution to evaluate V2x 2х - х* |

A: Given I=∫dx2x-x2If we consider x=1+sinθ and dx=cosθdθthen,I=∫dx2x-x2=∫cosdθ2(1+sinθ)-(1+sinθ)2

Q: 4-y² ²) dædy 2 2

A:

Q: Q5: 6y²dx-x(2x² + y)dy == 0 (Linear BernoullLeq.)

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Q: ų (H)= - 2y, (t) + 24;(4)= Y,(4) - 2y, (t) +2t t 9,lFS +2

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Q: 2.3 - y 5e2, with y(0) = 0 and y'(0) = 1 %3D

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Q: + Vs + es +- ds n = 3 From left endpoint s² + 1

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Q: 523 + 222 – 5 y = dy then dz 3x + 2

A: Consider the provided equation, y=5x3+2x2-53x2+2 Find the derivative of the equation with respect to…

Q: Q = - ST 8-x²-y² x² + y² y dz dx dy

A: