(D² – 9D)(D² – 8D + 7)y = 0 |

Q: (D² +D- 1)² y = 0 , when x = y = 0 , y' = y" = 1, y" = -1 %3D

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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: d²y dx2 -y = 10sin²x

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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: (2D2 + 3D – 9)X + (D² + 7D – 14)Y = 14..... (D + 1)X + (D + 2)Y = -8e2t 1 2 唱( %3D

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

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Q: (D3 - 3D - 2)y =0; when x =0, y=0, y' = 9, y” = 0.

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Q: -. (D² +4D+4)y=-x*e y =-x³e

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Q: D2 – 5D +6)y=3xex+2x2 , y(0)=0,y,(0)=1

A: Given differential equation is homogeneous ordinary differential equation. To solve this equation…

Q: 3t y" - y' - 6y = t²e³t - 4t², y(0) = 0, y' (0) = -1

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Q: 4. (D² – D – 6)y = 0; when x = 0, y = 3, y' = -1 %3D

A: Use this auxiliary equation and complementary function

Q: c. The f'(3) for y = v3x² + 9

A: c)y=3x2+9

Q: (D³ – D)y = –2(1+x) + 4e* – 6e¬* + 96e3x -

A: Given- D3-Dy=-21+x+4ex-6e-x+96e3x To Solve- The above differential equation.

Q: y²-6x²y=-9x ; y' at (1,3)

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Q: So* - y-³) dy 2.

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Q: æ = 4;y = t-1»Y t² – 1|

A: Use the following derivative formulas:ddxxn=nxn-1ddxfxgx=ddxfxgx-ddxgxfxgx2ddx ( f(g(x) ) = f'…

Q: · (D² + 3D + 2)y = xsin 2x

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Q: (D³ -3D* +4D³ -8D² +16),y = 0

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Q: d²y Find dx2 if –10x – 6y = -6.

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Q: y = (t² – 2)². a²y = t2 dx²

A: Derivative Question

Q: (D5-11D4+19D³ + 115D² - 200D - 500)y = 0 Ans: y = C₂e-2x + C₂xe-2x + C₂e³x + ₂x³x + C5x²e³x

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

A: Given that: y=4x3+3x2

Q: D² + D – 1)²y = 0 ,when x= y= 0 , y' = y''' = 1 , y" = -1

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Q: (D³ – D)y = 4e * + 3e2* %3D y" = (-Axe* + 3Ae*) + 8BE2* %3D

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Q: 14. (D - 3D² - 6D + 8) y 3.x = xe

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Q: 6. (D3 – D)y = -2(1 + x) + 4e* – 6e-* + 96e3x

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Q: [D³ – D)y = -2(1+x) + 4e* - 6e¬* + 96e3× %3D

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Q: d²y x-9 Find for y dx2 = (3x² –2x+5)

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Q: d²y + 4y = 8x² ,y(0) = -3,y'(0) = 0 dx2

A: We have to solve the differential equation using initial conditions.

Q: (d) y" – 6y" + 11y' – 6y = e2" (5 – 4x – 3a²)

A: Given  A non homogeneous differential equation in question 2. D.

Q: (D* + 6D3 + 9D²)y = 0 A. y = c1 + c2x + Cze 3x + C4xe¯3x + C4xe-3x B. y = ce* + c2xe* + c3e3* +…

A: Given DE is (D4+6D3+9D2)y=0.....(1)

Q: (D² +D-1)²y= 0 ,when x= y= 0, y' = y" = 1 , y" = -1

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Q: y = (t² – 2)². a²y 2. dx²

A: y=t2-22 and x=t2 Now, differentiate the given function with respect to t.…

Q: . (D²+1)y= 10e²x When x = 0, y = 0, y' = 0

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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: (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: (D3 – 2D2 – D + 2)y = 10sin2x – 5cosx - -

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Q: y' +2y = -x8y5 will be transformed to the follo"

A: Given: - The Bernoulli's equation is, y'+3xy=-x8y5 To transformed: - The given Bernoulli's equation…

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

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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: d4y Q4\ b) Find : Y=3X³-4X²+7X+10 dx4

A: Given: Y=3x3-4x2+7x+10

Q: (D³ – 4D² + 4D)y = 0 (4D² – 6D + 1)y = 0 %3D

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Q: 3. (D² – 3D + 2) y = 2x³ – 9x² + 6x

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Q: d²y Find for y dx2 x-9 (Зx2-2х+5)

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 3. (4D +4D2 + D)y = 0. 7. (4D3 - 3D+ 1)y = 0.

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Q: d²y x+2 for y=- X-3 8. Find dx2

A: Differentiate with respect to x.

Q: 6. (D³ + 2D²)y = 0; when x = 0, y = -3, y' = 0, y" = 12

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Q: 4. (D² +D-1)²y = 0 ,when x= y = 0 , y' = y" = 1, y" = -1

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