2. (D3 + D2 - 2D)y = 0 %3D

Q: y' + 2y = e*,

A: Note: Since you asked multiple questions, I solved first one if you want answer of other questions…

Q: (2x – 5 y dx + (- 5.x + 3y² kdy = 0||

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Q: y" + 2y' +y = e-*

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

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

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Q: rx dydx Vx2+y2 0.

A: We solve this double integration problem by substitution method as given below in solution

Q: dy ニ 3 x +y-2

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Q: Integrate the FF 2) dv Y Cy+z2)

A: We will integrate function of V=v w.r.t. v and function of y w.r.t. y and

Q: Find d2y/dx2 implicitly in terms of x and y.    x2y − 4x = 5

A: To find the second derivative of y implicitly in terms of x and y.

Q: 1. (D³ + 3D² - 4D - 12)y = 0 2. - d'x 19+ 30 = 0 dt3 dt 3. (4D4 - 8D³ - 7D² + 11D + 6)y = 0

A: 1). From the given differential equation; D3+3D2-4D-12y=0 So, The auxiliary equation is:…

Q: d'y 4x dx2 dy +6- + у %3D0 dx

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Q: y² (y + 2)ï dy

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Q: d³y 4. dx3 d?y dy -2- dx2 + 4 – 8y = 0 dx

A: The given differential equation is; d3y/dx3 -2d2y/dx2+4dy/dx-8y=0.

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: Find d2y/dx2 in terms of x and y. x2 + y2 = 3

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

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Q: dy 2x y3 – 4y dx II

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Q: d²y Find xp y = d²y 口 %3D dx 2.

A: topic - double derivative of a function

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

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Q: y= 2x3-14x2 +9x+7 dy %3D dx

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Q: ) y( 3x*- xy - 7)d -x ( xy ty- 2x) dgy = 0

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Q: z· 3°dz

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

A: Given that: y=4x3+3x2

Q: د؟ لر ول 3 y3 Xe dydx

A: We have to integrate the function fx, y=x3ey3 within the given limits of integration but the…

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

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Q: Find d2y/dx2   e4y+x=8y

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Q: d'y dy y = aebx is a solution of %3D dx2

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Q: dy 4x2 + x dx y + 4

A: Given : dydx = 4x2+xy+4

Q: 3. D'y - D'y- Dy + y = 0 (AD4

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Q: d³y d²y 4. dx3 dx3 dx -dy + y = 0

A: Consider the given equation. d3ydx3−d2ydx2−dydx+y=0 Now, make the characteristic equation.…

Q: Qs) y" + 3y' + 2y = e* – 3

A: See the details solution in below

Q: d?y Calculate dx2 y = -4x2 + 4x d?y dx2

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Q: 22 d'y dx² dy 7x- +16y=0 dx

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Q: Н. W.: -1/3 6dx 2. V9x2+ 1 c2/3 dy

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

Q: 4. (D3 – 4D² + 4D)y = 0 5. (2D4 – 3D3 – 2D²)y = 0 - -

A: (4). The given differential equation is: D3-4D2+4Dy=0 So, the auxiliary equation is: m3-4m2+4m=0

Q: 3 c2x S *x² dy dx 4.

A: Integral

Q: C:y 2x, x 8 ing (x² + y³)dx + (2xy +3)dy1

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Q: 4d³y-13 +6y=0 dy dx3 dx

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

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Q: d²y 10 + 9y = 5t, y(0 dx

A: Laplace solution: d2ydx2-10dydx+9y=5ty(0)=-1, y'(0)=2Taking Laplace on both sides we…

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: 2d²y -X dx² dx +y=(b+1)(b +2)x(In(x))

A: Given : x2d2ydx2-xdydx+y=b+1b+2xlnxb This is homogeneous linear diff. eq.

Q: d) y" -ry +3y = 0 %3D

A: Using power series method.

Q: y4 +y² - y +y 1 dy

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Q: Obtain the solution (D³ - 2D + D- 2)y = 0 d'y/dx? – dy/dx – 6 = 0 ; when x=0, y=0 and when x=1, y =…

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Q: y² (y + 2)ã dy

A: