– 2xy²e*´+6x²e" + (In x– 2ye*²+2x³e³ – 3 cot²y) dy=0 Find the general solution to the exact DE A y In x- y?e**+2x³e* + 3cot y +3y =c y In x-x²e*+2r²e' + 3cot y – 3y =C y In x- x?y?e**+ 2r³e" – 3cot y – 3y =C (D y In x- y?e*+3x?e' + 3csc y =C

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Q: Qs: Solve the fallow ing differential equations 2.

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Q: Give the general solution of the differential equation y"- 8y'+ 16y=5 e**cos(4 x) 4x 5 a) O y-q, +…

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A: Option (A) is correct.

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Q: Eliminate the arbitrary constant. 1) y = Bx + B² + 1 Answer: y = y'x + (y')²+1 -a DE of 1* order and…

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Q: 7 y' + y/(1 – x) = x² – x 9 xy' + (1 + x)y = e¯ * II (x – y) dx + x dy = 0 -

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Q: 4. Which of the following is the general solution of the differential equation x dy + y dx = x^2 dx?…

A: Note: As per our guidelines we are supposed to answer only one question if there are multiple…

Q: 3. Use your solution from Part 2 to give solutions to the IVPS i. y" + 2y' + 16y = cos 3t, y(0) =…

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Q: D) (3x² – 2y + e*+Y)dx + (e**y – 2x + 4)dy = 0 (Exact) E) (2xy*e" + 2xy³ + y)dx + (x²y*e" –x²y² –…

A: Let us consider the differential equation of the form Mdx+Ndy=0 The equation is exact if ∂M∂y=∂N∂x…

Q: The solution of the nonhomogeneous DE y" – 2y' +1 = 3e3x is y = cqe* + c2xe* + 3x y = cqe2x + c2 +…

A: We need to find the solution to the nonhomogeneous DE y''-2y'+1=3e2x⇒y''-2y'=3e2x-1. The…

Q: 3. Eliminate the arbitrary constants c, and c, from y =c, +C,e* y" - y +x = 0 c. y" - 3y' = 0 a. b.…

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Q: Let x, y be the unique solution of x' = y y' = 0, y(0) = 1. = -x x (0) Show that x, y verify x2 + y?…

A: Given x' = y                   (1)y' = -x                (2)x(0) = 0                    (3)y(0) = 1…

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Q: نقطتان )2( What is the Form of the General * ?Solution for this equation A. y(x) = Aem; + Bem;x dy?…

A: Given,  dy2dx2+dydx-6y=0

Q: 1) y'- Sy of(4) t? ostL 2 ミf flel= ylo) =1 2) y"t Uy = ule - 2). sint y(0)=1 y'Co) =O >) F (t) + 2 S…

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Q: (x + 2) y' = xy + 23-3x-6, when x 0, y 1 O y = 2-e O y = 3- 2e* O y = 1+2e* O y = 3+ 2e * %3D

A: Solution of differential equations

Q: general solution DE Xy" +y'+xy=o Find the of on co ∞)

A: The given differential equation xy″ + y′ + xy = 0, known as Bessel’s equation of order zero, has the…

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Q: Which of the following nonhomogeneous equation cannot be solved the method of undetermined…

A: If the term in the non homogeneous part is of the form eax, sinax, cosax, x,x2,..., xn, then the…

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Q: If y1 and y2 two solutions of (1 – a²)y" – 2xy' + n(n+1)y = 0; -1<x < 1 Show that W (y1, Y2) : 1-…

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Q: A particular solution of y"+2y' - 3y = 1 + xex.

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Q: What is the Euler equation associated with the Lagrangian L(x, y, y' , y") = 2x(y/")² – y²? O y+ 2y"…

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Q: - 2xy²e*² + 6x²e* \dx + (In x – 2ye*²+ 2x³e" – 3 cor'y) dy=0 Find the general solution to the exact…

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Q: y sin 2x + cos 2y = ax Find y' a – y cos 2x y% = sin 2x – sin 2y а - 2у сos 2x y sin 2x – 2 sin 2y…

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Q: Find the general solution of the inhomogeneous second-order linear ODE 2( 24" - 5' 3u)= 2(10 sinx)

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Q: 3. y" +3y" + 3y' ty :e-x - ylo) =o yto y" lo) y" la)= 2

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Q: Find the linear, nonhomogeneous differential equation with constant coefficients whose solution is y…

A: Given: yt=c1et+c2e2t-3tet+cost-e-t2          ...... (1) Solution: Differentiate equation (1) with…

Q: Using D-operators, the differential equation y"-xy'+ 2y – cos 5x can be written as: A (2D?– xD…

A: Please refer the attached image for complete solution. THANK YOU.