15. x dx + sin² (y/x)[y dx – x dy] = 0. ANS. 4x In |x/c| – 2y + x sin (2y/x) = 0. %3D

Q: (a) cos 22t – cos 12t = -2 sin 17t sin 5t (b) The Wronskian of f(t) = et and g(t) = est is W(f, g) =…

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Q: ANS. 2y arc tan ( 18. y? dy = x(x dy – y dx) e*l». A

A: Use integrating factor to solve it.

Q: Activity #2 in Differential Equations Solve for PS for the following differential equations. Make…

A: We will find out the required general solution.

Q: Solve the differential equation. (Use C for any needed constant. Your response should be in the form…

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Q: 1. cos y (y2 – 4x) dx + (2yxcosy – siny)dy 2. (sinxsiny + xsinxcosy – cosxcosy)dx – (cosxcosy –…

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Q: y' = cos?x cos y %3D

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Q: Consider the differential equation ex dy gy + dx X (x > 0) - x⁹ (a) State the form of the…

A: The given differential equation is dydx+9yx=exx9 with x>0 The solution to the given question is…

Q: 1.SECOND ORDER DIFFERENTIAL EQUATION Solve the equation d?x dx -2 + 2x 85 sin 3t dr? dt given that…

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Q: a.Show that the given equation is homogeneous. b.Solve the differential equation. c.Draw a direction…

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Q: (D2 — 9)у %3D Зех + х — sin 4x

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Q: E(0,+0) defihed in the Pange +2y= sin(x) + e* The differential equation dx dx ) Write the type and…

A: given differential equation isd3ydx2-3dydx+2y=sin x +e-2x

Q: Problem 2: (2y cos a + sin x) dæ sin a dy when a = , y = 1

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Q: 1. (х2 + у? + 3)dx — 2хydy 3D 0

A: As we know that: The differential equation Mdx+Ndy=0 is said to be exact, if ∂M∂y=∂N∂x. The solution…

Q: 17. [x – y arc tan (y/x)] dx + x arc tan (y/x) dy = 0. ANS. 2y arc tan (y/x) = x In [c²(x² +…

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Q: Find the general solutions of the following differential equations. d (dy 1. dx dx = 6 x + 3 4ト.0+-}…

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Q: sin 2y dx - 3x--cos 2y dy = 0 by separation of variables. Solve the differential equation A xe - 3…

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Q: 17. [x – y arc tan (y/x)] dx + x arc tan (y/x) dy = 0. %3D ANS. 2y arc tan (y/x) = x In [c2(x² +…

A: 17) The given differential equation is: x-y tan-1yxdx+xtan-1yx dy=0⇒xtan-1yx dy=-x-y…

Q: 2 y Siny-ay Scanned with CS CamScanner

A: Linear differential equation,

Q: Determine all the singular points of the given differential equation. (02 - 2) y" + 3y' +(sin 0)y =…

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Q: ´sin 2y dx - 3x¯-cos 2y dy = 0 by separation of variables. Solve the differential equation (A) None…

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Q: 4. tan x dy + y sin² x dx = 0,when x = 0, y = 1 у? (3 — сos 2x) %3D 2 о у(сos 2x - 2х) %3D 1 o y (2…

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Q: Bernoulli Differential Equation .3 A.) V +y°cos (x) +y cot (x) = 0 B.) y'+y = xy², ylo) = I こ

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Q: 20. y dx = (x + y² – x²) dy. arc sin (x/y) = In |y/c\. ANS.

A: topic - differential equations

Q: QUESTION 7 (Cauchy- Euler Equation): Find the general solution of the following differential…

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Q: II. Numerical Methods. Using h = 0.1, approximate the value of y when x = 1.5 for the given…

A: Solution:

Q: 16. (x – y In y + y ln x) dx + x(In y – In x) dy = 0. %3D ANS. (x – y) In x + y ln y = cx + y. 17…

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Q: ANS. arc tan (9/X) 18. y? dy = x(x dy – y dx) e*». ANS. y In ly/c| = (y – x) e*/».

A: (18).   The given differential equation is: y2 dy=xx dy-y dxexy

Q: 34. The differential equation x^2 dx - (y+1) dy = 0 is a First order homogeneous differential…

A: As per the company's guidelines we are supposed to solve first question for you, kindly repost other…

Q: d 2. dy 12; y=0, Y = 0 when x dx 1 dx dx

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Q: QUESTION 3 auchy- Euler Equation): Find the general solution of the equation for the differential…

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Q: (siny-ysinx) dx +(cosx +xcosy) dy =0

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Q: cos(x) cos (x) – 1 dy What is the general solution to the differential equation dr A y= - cot(x) –…

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Q: 1. Solve the differential equation of order one. Show your solutions. y' = x - 2y STEPS: a. Put…

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Q: [x – y arc tan (v/x)] dx + x arc tan (y/x) dy = 0. ANS. 2y arc tan (y/x) = x In [c²(x? + y²)/x*].

A: The solution is as follows :

Q: The equation below is a general solution to a homogeneous second-order differential equation ay" +…

A: Given differential equation is                                                  ay''+by'+cy=0…

Q: 1. Solve the differential equation dy dr sin(2r)sin (x) = 0, y(0) = 1 2. Consider the following…

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Q: B. EXACT EQUATIONS Find the general solution of the following differential equations dx (2) 3y sin x…

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Q: Activity #2 in Differential Equations Solve for GS/PS for the following differential equations. Make…

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Q: Differential Equations: Solve the given initial-value problem.. d^2y / d theta^2 + y = 0,   y(pi/3)…

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Q: 2. Solve the given the equation using the integrating factors found by inspection. [2х + усos(ху)jdx…

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Q: 1. cos y (y? – 4x) dx + (2yxcosy - siny)dy 2. (sinxsiny + xsinxcosy – cosxcosy)dx – (cosxcosy –…

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Q: dy - 4 cos 2x = -2y, y ) dx = 3

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Q: 3. Determine the Differential equations that you could solve using Separation of Variables,…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: C. Under Exact Differential Equations. Determine whether each of the following equations is exact.…

A: Given that: 1. (2y2-2xy+3x)dx+(y+4xy-x2)dy=0

Q: 4. [cos(2y) – 3x²y²]dx + [cos(2y) – 2x sin(2y) – 2x³y]dy = 0 when x = 0 ; y = 0

A: According to our guidelines , we are supposed to answer only first question. Kindly re-post other…

Q: y = c, cos(5x) + c, sin(5x) is a two-parameter family of solutions of the second-order DE y" + 25y =…

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Q: 1 sin ax = S(D) S(-D) sin ax f(ai)f (– ai) 40. f(ai) f(-ai) # 0.

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