(D² + 49)²y = 0 (D² + 36)²y = 0

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

A:

Q: (D3 + 4D² + 9D + 10)y = -24e* %3D

A: Let's find.

Q: D7 + D® – 2D$ – 2D4 – 7D³ – 7D² – 4D – 4) y = 0 - - - -

A: follow next step

Q: (D5+ D4-7D³ - 11D²8D-12)y = 0

A:

Q: (4D4 - 4D3 - 3D2 - 2D + 1)y = 0

A: We have to solve the given equation.

Q: 1. (D³ - 3D²D + 3)y = 0

A: To Solve: (D3-3D2-D+3)y=0.

Q: 7. (D² - 2D + 2)y = 0 8. (D² + 9)y = 5e* - 162x 9. (D² + 9)y = 5e% - 162x?

A:

Q: 1. (D² -5D³)y = 4 2. (D³ – 5D* + 7D³ +D² -8D+4)y = 0

A:

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: [D³ 6D² + 11 D - 6) y = tanx -

A: Sol:- Original Differential Equation can be re-written as :- y''' -6y'' +11y' -6y=tanxThe general…

Q: -. (D² +4D+4)y=-x*e y =-x³e

A:

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

A: Use this auxiliary equation and complementary function

Q: 2 2X-) dy tf2 るメー。 2. Y+2

A: We have to solve the given differential equation.

Q: d2y Find anž if 2x²-3y²=7 dx2

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

Q: 2 y (4- y²)³ dy

A: The objective of the question is evaluate the definite integral.

Q: V 96x-x² 48 9Vx2+y2 dydx =

A: Refer to the figure shown below:

Q: (D² – 9D)(D² – 8D + 7)y = 0 |

A: We have to find the solutions of the given differential equations

Q: Find d² y dx² for x³ + y³ = 2 43

A:

Q: d²y Find dx2 if –10x – 6y = -6.

A:

Q: y = (t² – 2)². a²y = t2 dx²

A: Derivative Question

Q: d2y/dx2, where y = 4x3/2

A: Given- y=4x32 To Find- d2ydx2 Identity Used- The power rule of derivative ddxxn=nxn-1

Q: 10. (D² – 3D) y= 9x² = 9x2

A: 10) Given Information: Given differential equation is D2-3Dy = 9x2

Q: (D³ - 3D2 + 9D + 13)y = 0

A:

Q: 14. (D - 3D² - 6D + 8) y 3.x = xe

A:

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

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

Q: (D³ – 3D + 2)y = -7 у" - 9y' %3D 27

A: (1).    The given differential equation is: D3-3D+2y=-7

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

A:

Q: C2 (2+/4-x2-y2 (x² + y² + z²)/² dz dy d /4-x² J2- 4-x²-y2

A:

Q: (D² + 3D – 4)y(x) = 12e2x

A:

Q: (D³ - 3D² - 6D + 8)y = xe

A:

Q: 5. (D4 + 2D3 + 10D²)y = 0

A:

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

A:

Q: 6. (D² + 1)y =- 1 %3D 3

A:

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

A:

Q: 2x + 글y=D2 %3D

A: Given,          The equation is 2x+12y=-2.

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

A:

Q: (D6 – 3D5 + 3Dª – D³)y = 12

A:

Q: dy - 2ry = r'²

A:

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

A:

Q: (D² – 3D – 4)y = 30e4* -

A:

Q: d*y d³y - 4· dx3 +7 d²y 14 dx4 dx2

A:

Q: y" - y' - 6y=t²e³t — 4t², y(0) = 0, y' (0) = -1

A:

Q: (2D* + D3-4D2 - 10D - 4)y = 0

A:

Q: 3. (D3 - 4D2 + 7D)y = - 11

A:

Q: 2. (6x-2) dy d2

A: Given query is to find the value of the integral.

Q: d4y Find Y=3X³-4X?+7X+10 dx4

A: Given y=3x3-4x2+7x+10 To find d4ydx4 Formulae used : dxn=nxn-1 dc=0, where c is a constant.…