(D³ – 3D + 2)y = -7 5.

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

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Q: d²y dx2 -y = 10sin²x

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Q: 1. (D2 + 2D + 4)y = 8x? + 12e-*

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

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Q: 4. (Dª + 6D³ + 9D²)y = 0 5. (D4 - 5D² - 6D - 2)y = 0 6. (D5 - 5Dª + 7D3 + D² - 8D + 4)y = 0

A: NOTE:- As per our guidelines we are supposed to answer only one question as there are multiple…

Q: (D³ – 2D² – 3D) y = 0

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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: -. (D² +4D+4)y=-x*e y =-x³e

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Q: Q3 المطلوب ایجاد حل المعادلة التفاضلية التالية باستخدام تحويلات لابلاس: y" - 3y' + 2y = 4e2x, where…

A: Given that  The differential equation  y''-3y'+2y=4e^(2x)

Q: D°y +3D?y+2Dy = 3e-2* ||

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

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Q: 5. (D4 – 2D3 + 2D² – 2D + 1)y = 0 |

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Q: y = (t² – 2)². a²y = t2 dx²

A: Derivative Question

Q: (D2 − 2D + 1)y = 0

A: Given: D2-2D+1y=0 we know that a2-2ab+b2=a-b2

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

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Q: 10. ( Dª – D³ – 3D² +D + 2 )y = 0

A: Solved below

Q: (D³ - 3D2 + 9D + 13)y = 0

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Q: - y² dy 3y 50.

A: Simplify the expression and integrate it.

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

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Q: (D²+4D+5)y=35e : y(0)--3, y'(0)-1

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Q: 9. (D²+4D+5)y-35ex:y(0) --3, y'(0) - 1

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Q: 14. (D - 3D² - 6D + 8) y 3.x = xe

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

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Q: Dª + 4D³ – 3D² − 2D + 1)y = 0

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Q: (D² – 6D + 9)y = 0 ; x = 0; y = 0; y' = 2 %3D %3D

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

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

Q: +(ux+y-3) dy=D0 Q=Ap(5-人+以り)+ Xp[^ーメ2)

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

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Q: (D³ + 3D² + 3D + 2)y = 0

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Q: (D3−D2+4D−4)y=0 ; y(0)=2, y'(0)=7, y"(0)=-3

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

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Q: Find d?y/d?x from x=t2-3t+4 and y=t2 +4t -5.

A: The parametric equations are x = t2-3t+4 y = t2+4t-5 To evaluate: The expression of d2ydx2 Formula…

Q: (D³ - 3D² - 6D + 8)y = xe

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

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Q: Find the solution. (D³+3D²– 4D)y = 0

A: The Auxiliary equation is D3-3D2-4D=0 solve for D D3-3D2-4D=0 DD2-3D-4=0D=0 or D2-3D-4=0 now…

Q: Find the solution. (D2+4D+4)y=0; when x =0, y=1, y'=-1.

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Q: (D6 – 3D5 + 3Dª – D³)y = 12

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Q: (D2-3D+2)y=xe*.

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Q: dy - 2ry = r'²

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

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Q: (D³ + 2D*)y = 0 y(0) = -3 , y'(0) = 0 and y"(0) = 2

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Q: Yt = Yt-1 + 2yt-2(Yt-3 – 1) %3D

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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: y? -dy (y2–4) 7

A: We have to find solution

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

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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.…

Q: 3x + 8 y = - y' =D %3D y'" =D

A: We can find the first and second derivative of the given function as below.