1. Consider the differential equation: (x cos y) dy + (x + 3x sin y) dx = 0. (a) Show that this differential equation is not exact. a + B+1 (b) Show that u(x) is an integrating factor for this equation. (c) Find the general solution of this differential equation.

Q: B. Determine the form of a particular solution for each differential equation 1. y" – 2y' + y =…

A: Find your answer below

Q: 4) Consider the differential equation (3xy+ y²) dx + (x² + xy) dy = 0 (a) Determine whether the…

A: For the differential equation 3xy+y2dx+x2+xydy=0 The objectives are: (a) Determine whether the above…

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

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Q: 1. Find the general solution of the differential equation (1+ 9x²) cos y dy – 3(1+ sin y) dr = 0.

A: we have to solve this by separation of variable

Q: 2. Solve the ordinary differential equation. a) e2*cos(y)sin(x)dx + e*tan(y)dy = 0 b) (x* + 1)dx -…

A: To solve the following problem we use the seperation of variable method and also use  standard…

Q: Solve the differential equation: [y³ – y²e* – cos(x – y)]dx + [3xy² – 2ye* + cos(x – y)]dy = 0 ;…

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Q: Determine the values of r for which the differential equation y + 2y = 0 has solutions of the form y…

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Q: 6. Solve for the general solution of the differential equation using exact equation [2x + y cos…

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Q: 1. Solve the differential equation y(x +y) dy 2 dx "homogeneous" x2 with y(1) = –1.

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Q: 4. Find a third-order linear homogeneous differential equation which has the function r(t) = 3e-t +…

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Q: 1. A solution for the differential equation is y = e"x A, sin (vx) + A, cos (vx), where m and n are…

A: Let's find.

Q: [6] Find the solution of the first order ordinary differential equation (1– 3y2) dy – x sinx dx=0, y…

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Q: 1 xdy – y(1+ y cos 2x)dx = 0 ;y(0): Ans: 2x + y sin 2x = 0 2

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Q: Find the particular/primitive solution to the differential equation (y+y cos x - yex)dx+2(x5+ln x -…

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Q: 1. Determine the value of C for the given first order differential equation when x=2 and y=1. Show…

A: Recall: An equation of the form Mdx+Ndy =0 is exact if ∂M∂y=∂N∂x and its solution is            ∫y…

Q: Consider the differential equation: 1. y"-y%D What is the general solution? y= [a + In(1 +te *)]e* +…

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Q: y = G, cos 3x – C, sin(-3x)

A: The general solution of a differential equation is y = c1cos(3x) - c2sin(-3x) We need to find the…

Q: 1. A solution for the differential equation is y = e"* A, sin (vx) + A2 cos (vx) , where m and n are…

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Q: Find a particular solution y, of the differential equation: y" + 9y = 2 cos 3x + 3 sin 3x

A: Explanation of the answer is as follows

Q: (b) Consider the differential equation ydx + x(lnx-lny - 1)dy = 0. Hence, or otherwise, use an…

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

Q: -The Bernoulli's form of the differential equation 2x'dy-y(y² +3x)dx=0 is

A:

Q: The Bernoulli's form of the differential equation x²dy+ (2xy-y³dx=0 is The Bernoulli's form of the…

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Q: x2+1 y'= Ans: y = + x + In(x – 1)² +c = -X - X-1

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Q: (b) Consider the differential equation ydr+r(lnx-lny - 1)dy = 0. (i) Show that the equation is a…

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Q: 3. (a) ! Show that the differential equation (r2-y2)dx-2rydy 0 is exact. (b) . 1 Find the general…

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Q: 5.- Use the method of undetermined coefficients to find a particular solution, Y, , for the given…

A: Take up in perfect form and put on the given differential equation

Q: 1. Find a homogeneous linear differential equation with constant coefficients whose general solution…

A: y=c1cosx+c2sinx+c3cos2x+c4sin2x For c1 and c2 α=0, β=1 α±βi0±1i0±i m-im+i=0m2+i2=0m2-1=0

Q: Consider the differential equation y" – 2y'+ 37y = 0; e* cos(6x), e* sin(6x), (-o, ). Verify that…

A: y(x) = ex(C1cos6x +C2 Sin6x)

Q: 7. Find a linear differential equation with constant coefficients Ly = 0 such that y(x) = cos(x) +…

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Q: b) Euler's method is used to solve a first-order differential equation dy dx from x = 0 to x = 4

A: We need to write Euler's method to solve the differential equation: dydx=f(y,x), from x=0 to x=4.

Q: Find the general and special solution of .the differential equations X cos^2 Y dx +tany dy=0

A: By Separation of variable we can solve the problem.

Q: B2. Find the general solution of the linear differential equation. (tan-ly-x) (1+y²) dx dy

A: Concept Used: A first order differential equation is said to be linear differential equation if it…

Q: (2) Consider the differential equation = x+sin y. dy dx A (a) A solution curve passes through the…

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Q: Q-2) [CLO1(PLO1)] Solve the given differential equation subject to the indicated initial condition a…

A: 2) Given differential equation is  α +11 + y2 + cosx - 2xydy - yy + sinxdx = 0,   y(0) = -1

Q: Consider the non-exact differential equation (12 + 5xy)dx + (6xy−1 + 3x2)dy = 0 (a) Show that…

A: The given equation is the non-exact equation:

Q: 3. Using the steps in solving for homogeneous differential equations, evaluate: dy x² + 2y² dx ху

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Q: 12) Consider the differential equation y" + a1(x)y' + ao(x)y = 9 sin(7x) And suppose that Y1 = x Y2…

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Q: 1. Find the general solution of the differential equation 1 sin z y*y' + =y°

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Q: Q-4. Form the first-order differential equation of y = e(sin y+z) %3D

A: We have to find the first order derivative first.

Q: How does the following differential equation (y+2xy*) dx + (1+ 3.x²y² + x) dy = 0 satisfy the…

A: When the partial differentiation is done with respect to a specific variable, then all other…

Q: Find the general solution of the first-order linear differential equation (y + 1) cos x dx − dy = 0…

A: We have to find general solution of the first-order linear differential equation: y+1 cos x dx-dy=0…

Q: 2. (x+2y-1)dx - (2x + y - 5)dy = 0

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Q: 2. Determine the general solution of the given Differential Equation (x2 – xy + y?)dx – xydy = 0 - -

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Q: 1. Solve the differential equation (x+y)'dx+(2xy +x -1) dy =0 subject to the initial condition y(1)…

A: Compare with exact differential equation and then check exactness

Q: 4. Find the general solution of the differential equation using the method of undetermined…

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Q: 1. a) A non-linear ordinary differential equation is given as: dy (cos* x) + y (sin x) (cos³ x) – y³…

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Q: 11) Consider the differential equation: xy'/(x5+9)y = cos(x) + e6x/y. Put the differential equation…

A: Here given differential equation as

Q: 1. In the differential equation (x+2y-1)dx+(2x+4y-3dy -0, we let the substitution

A: In the differential equation (x+2y-1)dx+(2x+4y-3)dy=0. we let the substitution W=?

Q: 1. Given the following differential equations (DE): A. e*y' = x – 2y в. у'— еУ %3D sin x Identify if…

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