2. Solve the differential equation: (y² + xy°)dx + (5y² – xy+ y° sin y)dy = 0 by finding an appropriate integrating factor. Hint: Inexact equation.

Q: 2. Solve the Second order differential equation d'y dy -4 +11y=e* sin 4x. dx dx?

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Q: y' - 5y = -xy, y(2) = 1 %3D

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Q: The general solution of the differential equation d’y dy dx 2 -X-+Y3D2(nx dx

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Q: Find the solution to the differential equation =(2x + y cos xy) dx + x cosxydy = 0

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Q: Calculate the value(s) of C for which y=x'-2C is a solution to the differential equation dy -3y-54 =…

A: We have to find the value of C

Q: y'dy-(4y + 48x kdx = 0

A: Let us consider the linear non homogenous  first order differential eqaution of the form  dydx+p(x)…

Q: (6) Solve the homogeneous differential equation (x – y)dx – 2xy’dy = 0 - |

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Q: (b)Solve the differential equation : 1+y? %3D 2+3x dy with the initial condition y () = 0. %D dx

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Q: 1. Find the general solution of the differential equation: d°y d'y dy , dy - - dx6 dæ3 dx2

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Q: Determine whether or not y=C1 cos (2t) + C2 sin (2t) is the solution to the differential equation…

A: we check y=c1 cos(2t)+c2sin92t) is the solution to the differential equation y''+4y=0

Q: 7. 1 (x dy – y dx) = 0 x² + y?

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Q: 2. Find the particular solution to the differential equation dy 2y? dx cosec (x) if the point…

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Q: (4) Find the general solution of the differential equation (D² + 2D + 5)Y = = cos ha

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Q: 1. Solve the following Exact Differential Equation : dx 3 1 (2?y3 - + y = 1 1+ 9x2' dy

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Q: a) Solve the following first-order differential equations: dy = -y 2x, given that when y=0, x=+2 dx

A: We have given  -y dy/dx = 2x when y = 0 and x = +-2

Q: Solve this exact differential equation. (e2y-ycos xy) dx +(2xe2y -x cos xy + 2y) dy = 0.

A: We have the differential equation e2y-y cosxydx+2xe2y-x cosxy+2ydy=0 A differential equation of the…

Q: 11. Solve the second-order differential equation y" – y' – 2y = 20 cos x using the method of…

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Q: Find the general solution for the differential equation: 1- y" - 4y = 1+ 65e'cos(2t)

A: Given : y'' - 4y = 1+65et cos(2t)  To find : General solution of the given DE

Q: What is the complementary solution y, for the differential equation y"- 4y=12x A y,=c,cos 2x + c,sin…

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Q: 1. Find the general solution of the differential equation cos x 1. dy 2 y2-4 dx 2y

A: Solve differential equation by seperation of variable:-

Q: The degree of the differential equation (y")³ + y' – cos y = х is с. 1 d. no degree а. 2 b. 3

A: Degree of the differential equation is the highest power of the highest order derivative involved in…

Q: Consider the differential equation d'y dy dx² dx -6y = 0. Enter either of the solutions of the…

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Q: 4. Find the general solution of the differential equation given by y' – xyʻ +x = 0, where yf = dy/dx…

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Q: (a) Solve the second order differential equation below: d?y dy - 7 +10y = 4e3x dx dx?

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Q: y' +2- Jy = 0, y(1) = 0

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Q: Solve the given differential equation (D -3D+2)y=xe* +sin2x

A: We will find out the required solution.

Q: 4. Solve the homogeneous differential equation x'dy+(y² +xykdx = 0.

A: To solve the given homogeneous differential equation.

Q: The solution of the differential equation below is dy 3y- + 4x = 0 dx %3D

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Q: b) Solve the differential equation y(1-ysin(x))dx + (2x+3ycos(x))dy=0.

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Q: 1.- Show that the equation is exact, then solve the differential equation: sin 2y dx + (2xcos 2y –…

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Q: Find an Integrating Factor, then solve the Non-Exact differential equation. (Non-anonymous question)…

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Q: (5) Find the solution of the following separable differential equation: dy -x(y + 2)², y(0) = 2. dx

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Q: Solve the differential equation 4y® ,6 dy 7xe-y' sin x? = 0 dx -

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Q: (5) Find the general solution for the exact differential equation (x² – 4xy – 2y2)dx + (y? – axy –…

A: The given differential equation is x2-4xy-2y2dx+y2-axy-2x2dy =0

Q: b. Solve the exact differential equation (9x* +5x*y*)dx +(4x°y° -7y° )dy = 0.

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Q: (5) Find the general solution of the differential equation (D² + 6D + 9)y = sin 3x

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Q: Solve

A: The solution is as follows below :

Q: 5. y sec?xdx - (1 – 2y?tanx)dy = 0

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Q: Find the solution to the differential equation below such that y(0) = 14 y' = 10xy - 2x y(x) =

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Find the general solution to the differential equation y" + 49y = cos (2x). %3D

A: Consider the given differential equation y''+49y=cos2x. The characteristic equation is m2+49=0. That…

Q: (d) Find an appropriate integrating factor for this differential equation and solve it downright, y'…

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Q: Solve the following differential equations: 1 dx + (y-2r) dy = 0, y(-1) = 2. (3-y) ry?

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Q: 6. Solve this homogeneous differential equation. [ (x² – y²)dx + xy dy = 0

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Q: 9. Find the general solution of the differential equation:(D² – 5D + 6)y = 100 sin 4x %3D

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Q: 3.(i) Solve the Non-linear differential dy equation dx y = 4 • XVG 1- x2

A: Consider the provided question,

Q: What is the complementary solution y, for the differential equation y"- 4y=12x (A y.=c,cos cos 2x +…

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Q: 1. Solve the differential equation dy y²sin(2x)sin²(x) = 0, y(0) = 1 dx - %D

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Q: y' - 5y = -xy, y(2) = 1

A: