(xiv) f(t) = 3+et – te-2t + e5t cos3t + 6sinh7t

Q: y" ~2y² + 5y = 4e²x cos2x

A: Solution of the non- homogeneous higher order differential equations.

Q: (b) J 32+3 22²-2-1 dx

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Q: (2rz - yz)dr + (2yz – zr)dy – (² – xy + y²)dz = 0.

A: Given that, 2xz-yzdx+2yz-zxdy-x2-xy+y2dz=0

Q: 7. Find d²y dx² from y = √√x- =√x-²/2

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Q: 6. Find h' (÷) , h" (), and h" (G), given h(r) = sin r cos 3r.

A: since you have asked multiple questions in a single request so we will be answering only first…

Q: 1. Solve the following first-order equation: (2.ry +3y?)dr - (2ay+a)dy = 0. %3D

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Q: Solve the following DE: (1+ y² + xy²) dx + (x²y + y + 2xy) dy=0 O 2x+y²(1+x)² = C O 2y² + x²(1+x)²=c…

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Q: (11) Evaluate [[3x+5y+i(x²-y') dz along y=x (0,0)

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Q: 1.n f csc n? de y2 - 2y + 3 2.5; Vy - 3y: + 9y – 21 dy

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Q: (x2 + y2 + x)dx + xydy = 0 %D

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Q: Find an expression for dy/dx. y= (u+5)(u-5) u= x2  + 7

A: Given expression are  y=u+5u-5=u2-52                                Using a+ba-b=a2-b2=u2-25…

Q: Use Green's Theorem to evaluate -15/4 O -218/3 O 19/2 [(6y - 9x) dy - (yx - x³) da where C' is shown…

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Q: 1 1-¹ ( ( 5 + + 2) ³) 3 = Find ac + b. α ~tbeat C

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Q: (a) /4 1+3 cos² 1 d.x; COST dx3B

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Q: 4. (D2 – 5D + 6)y = 15sinx – 15cosx -

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Q: 3. Solve the equation: (Dª – 1) y = 0

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Q: (a) y" + 9y = 6e3z

A: Note:-     as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: dy as a function of x. Write the function in the form y = f(u) and u= g(x). Then find y = (- 2x +8)…

A: We know that ,  if y = f ( u ) and u = g ( x )  Then  dy / dx = f ' ( u ) • g ' ( x )

Q: Determine the appropriate form for a particular solution of the fifth-order equation(D - 2)3 (D2 +…

A: Given differential equation is D−23D2+92y=x2e2x+xsin3x......1. We have to determine the appropriate…

Q: (2х — 8)dx 2 — 6х + 18

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Q: Differentiate the following:

A: Step 1:Step 2:Step 3:Step 4:

Q: dz (9-z2) 2 Select one:

A: We have to find the integral.

Q: find the general solution - こ (64y = sin (2x)

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Q: You are monitoring the movement of a 2D alien. After months of analysis, you have come up with a the…

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Q: e2" – e5r dr dx b)] Jx (1 + x) + e3r

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Q: Find the complete solution: (cos2y - 3x²y²)dx + (cos2y − 2xsin2y — 2x³y)dy = 0

A: Given data:  cos2y-3x2y2dx+cos2y-2xsin2y-2x3ydy=0 We have to find the complete solution.

Q: IxV In?x + 1 In x dx V In² x + 1

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Q: 1. a) Find , if y= (x² – 11)“ dx b) Express (8/30) (2Z60) in the form a+ bi c) Solve (2+3) +3/- x+iy…

A: The detailed solution is as follows below:

Q: given f (2) = 3z - 6z+ j3. what is the value of u(3, 2)

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Q: Operator 1/f(D) 5. (D2 + 16)y = 4sin3xcosx 6. (D – 1)²y = 3cosh²x

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

Q: Solve the ODE

A: Given ODE is y3+2y-1dy=y2-4y+83dx

Q: Suppose w = 8x² + 2y², X = 3 cos(t) + 9 sin(t), and y = 3 cos(t) — 9 sin(t).

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Q: (10) y "+10y "+34y '+ 40y

A: Introduction: A differential equation is an equation that contains the derivative of an unknown…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.