4. (D² + 4D + 4)y = 0 5. (D³ – 4D² + 7D)y = 0 |

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: d = V(22 – a1)° + (42 – Y1)² %3D - - (8, -3) and (-5, 6)

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Q: Vy - y 3 b) dy 2 y²

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Q: d²y 5. If y = 4sinx + x²cosx + 4x then find dx2

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

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Q: (D3 + 4D² + 9D + 10)y = -24e* %3D

A: Let's find.

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

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Q: d) (D3 – 3D2 + 4D – 2)y = e* -

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Q: 2) (D3 + 3D2 4D – 12) y = 0 (D) (E) (F)

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Q: dy Find if y 3e2 3z 一山 %3D O -9e 2

A: Using chain rule of differentiation.

Q: If x = 2t² + 3 and y = t* d-y – v2 then is 2 dx 1 a) 4 b) c) 2t d) None of These -

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Q: Q2. (a) dy = (x + y + 3)² (b) 2xy4 = 4x² + 3y?

A: Given that a)dydx=x+y+32 b)2xydydx=4x2+3y2

Q: 32 8y%dy y-15 2.

A: The given integral is,

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

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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: d'y d³y - dx5 dx3 = 24.

A: Solution :-

Q: y = x(2x+1), y" y = (4x − 3)¹/²2, d³ y dx³

A: Topic:- derivatives  Note :- as per our guideline if more than one question uploaded than only first…

Q: f(s) -3s² – 5 %D S f(s) -2 -1

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Q: d*y + 2 dx3 d³y , d²y 8. dx4 = 0 dx2

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Q: d2y Find anž if 2x²-3y²=7 dx2

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

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

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Q: Find d² y dx² for x³ + y³ = 2 43

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

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Q: 2x d³y d'y dx³ dx² 2 = d²y_a². dx2

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

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Q: dz (D2 + 16) (D² + 4D – 5) (D² + 2D - 3)*z = 0, Dz = dr

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Q: (D² – 5D) + 4y = 0 (D² – 9)y = 0

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Q: dy iven x² + 2y² = 9. Then, dx2 A 64x2 B) 4y3 O 32 xy 16 D 9y

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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: d²y if 2x²-3y²=7 dx2

A: Differentiating both sides of the equation. 23x2-32ydydx=06x2-6ydydx=06ydydx=6x2dydx=x2y . . . . . .…

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)

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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: (D² – 8D + 16)y = 4e¬v2t, y(0) = -1, y'(0) = 3;

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

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

Q: (D² + 6D + 7)(D3 – 5D² + 6D)y = %3D

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Q: d) y = - + 3 e) y = 20.5x f) y = V2(x – 6)

A: Given query is to find the transformation performed and then graph the function.

Q: d²y x+2 for y=- X-3 8. Find dx2

A: Differentiate with respect to x.

Q: d*y d³y - 4· dx3 +7 d²y 14 dx4 dx2

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

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Q: 1. (D* + D' – 7D® + D° + 22D* – 22D³ – 20D² + 40D – 16) y = 0

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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: (D² – 4)y = 2 – 8x; when x = 0, y = 0, y' = 5. %3D ANS. y = e2x – e-2* + 2x – }.

A: We have to find solution of given differential equation.

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: dx Vx²-4x-7 7. dy y2-8y+5

A: