Giren (1-2²) y" - 2my' + 2 c²+1 i) solve the equation at ii) (1) using Po (n) -2 (2+1)y= ห=0) other method, find P₁ (1) PCn) and P, C-1)

Q: q''+q'=2z2

A: In this question, we solve the differential equation q''+q'=2z2 By using the method of indeterminate…

Q: Solve y" – 2y' – 3y = 3t² – 5 using the Method of Undetermined Coefficients.

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Q: d) Solve: y"+y"-5y' + 3y = 0

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Q: Q7. Solve the Cauchy-Euler equation (i) 4.x²y" + 4.xy' – y = 0. (ii) 4x²y" + y = 0.

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Q: a) (3xy - y' + 2x) dx + (2xy 3xy + 1) dy = 0, y(- 2) = b) (ye* + 2e* + y²) dx + (e* + 2xy) dy = 0,…

A: A differential equation of the form M dx+N dy=0 is said to be an exact differential equation if it…

Q: h(x) = 4(2x – 3)*(2x – 5)³ , find h'(x). Factor Fully.

A: Given query is to find the derivative of the expression.

Q: u" - 16u = 0

A: Given the differential equation is u" - 16u = 0. Here the auxiliary equation is m2 - 16 = 0

Q: Solve y" – 4y' + 8y = e2" + sin 2x 3.

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Q: a) x2y"+ xy' +(x2- 25)y = 0 b) (1 - x2) y" - 2xy' + 42y = 0 %3D %3D

A: a. Bessel ordinary differential equation has the form of x2y''+xy'+x2-v2y=0. Now, Rewriting the…

Q: 2y" + 3y' - 2y = 3xez* - 2sinлx (Use Method of Undetermined Coefficients (MUC))

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Q: What are the solutions of the equation 2sin(4x)=1 on the interval [0,n)?

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Q: Find a real general solution x2y"+0.7xy′−0.1y=0

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Q: When you plug in (0,0,0) into 7x - 5y + z = 0. It holds true, however, when you plug in (1,1,1) into…

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Q: Solve (D5 – 2D4 + 4D³ – 8D²) y = 48e-2 16 sin (2x) - = A- B I = E E E P & O

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Q: b)- dx a(13-x)(2+hncr)) + Ja9 differentiating on both sides dy (13-2) (2+dnc) da b9 de + be9) %3D de…

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Q: 5) Solve y) - 3y4+3y" - 3y" +2y' = 0.

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Q: (ii) 42?у" + у — 0. 4.x

A: Consider x=et and differentiate to obtain the expression of dtdx . x=ett=lnxdtdx=d dxlnx=1x Break…

Q: Solve (x-1)' +(x-2)'+(x - 3)' +(x + 4)' +(x + 5)' = 0

A: The solution for the above question is as shown below.

Q: Solve for the particular solution of the given IVP: O (t^2+y^2)^1.5 - 3ty = 89 O (t^2+y^2)^3 - 3ty =…

A: The given initial value problem is: dydt+y-tt2+y2t-yt2+y2=0 ;       y(4)=3

Q: Ex. (9) Sol:- Solve 3y"-2y'+y= 4x+2

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Q: Solve Legendre equation (x + 1)2 dx2 + (x + 1) dy (2x + 3)(2x + 4) dx

A: Given equation is. x+12d2ydx2+x+1dydx=2x+32x+4                               ......1 Let…

Q: 5) x2. dx = x² + 3xy + y², (c) dr = 2 = 3v, + 3x' (d) (1 - y)' + By - 5x = 0.

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Q: Solve y"-3√²+2y=x,_ _y(0) = y² (0)=0 for the solution: Y'cAY+(x) P(D)= (6)

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Q: Determine the solution of the following differential equations: 1. ((4D^4) − (8D^3) − (7D^2) + 11D…

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Q: What is the special solution of the equation y0̅ ? y''' + 5y'' + 12y' + 8y =5sin2x +10x2 - 3x + 7

A: Find the attachment

Q: Differential Equations. 100 150 Very large tank initially contains of Salt Water Containing gallons…

A: As per the guidelines I did first question.

Q: Solve ²₂(x + 1)(x + 2)²(x² − 1)dx with and without the even-odd theorems (show both solutions).

A: ∫-22(x+1)(x2+2)2(x2-1) dx

Q: 11) Solve the given IVP, ""+12y" +36y=0, v(0) 0, '(0)=1, "(0) = -7.

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Q: -y(2x+y) x(x+2y) - y'=-

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Q: cosh (z) = eIz-e-iz 2i +e-iz 2i +e- 2 2

A: Use the standard formula of hyperbolic cosine function.

Q: |(r +x² +x+1)(3x* +4x° + 6x² + 12x + 1) dx (x3

A: Use the substitution method and simplify the integration first then integrate.

Q: Solve y" - 5y' + 6, using characteristic equation.

A: Given differential equation is y'' - 5y' + 6

Q: How do I explan that x2+4xy-Sin(y2) is not a quadratic form?

A: To justify that the given expression in x and y is not a quadratic form in x and y

Q: x + 1) ² − 4(x + 1) dx + 4y = 0. Given that y₁ = ²x is a solution; find the general solution. dy dx²…

A: Solution to the differential equation