4. What is the integrating factor of the first-order linear differential equation below? (y – 1) sin x dx + dy = 0

Q: 8. Use a substitution to solve the homogeneous 1st order differential equation (x – y)dx + x dy = 0

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Q: What is the particular solution to the differential equation = (x – 1)(1 y) with the initial…

A: givendydx=(x-1)(1-y)we will solve this equation by Variable separable method

Q: Consider the differential equation dy = x° (1 – y) with a particular dx solution y = f() having an…

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Q: 3. Find the general solution of this separable differential equation. dy y cos x dx sin x + 2

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Q: What is the integrating factor of the non-exact differential equation (4ху+ 3у?-х)dx + (x2+2ху)dy…

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Q: The integrating factor for the differential equation (3xy + y)dx + (x2 + xy)dy 0 is - X Y O - Y O

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Q: 2. Show that these differential equations are exact, then integrate to find the solution. (a) dy +y…

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Q: ive a general solution to the following differential equation: ya) – 2y" +y = x cos r

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Q: 9. For the differential equation condition y(0) = 1. dy -- y = ey², solve for y = f(x) given the…

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Q: 4. The degree of the differential equation (y")³ + y' – cos y = x is

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Q: Obtain the differential equation associated with the family of curves below: y = A + Bx + Ce2x y" -…

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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: dy y+x , У(1) -0.5 dx

A: Here first given in the question that h is 0.1 and y(1)=0.5 and a differential equation is given.…

Q: y' + y² = 3y tan x tan? x + 1

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Q: Given the non-homogeneous second order differential equation:: y" – 4y = sin(5æ) the general…

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

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Q: sin x sin y dx + cos x cos y dy = 0 %3D

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Q: Given the differential equation dy +y dx=2xy-e* dx what is the value of the integrating factor?

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Q: The integrating factor for the differential equation dy X- dx 4x cos(x)y = –5e* is e-4 sin(x) Select…

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Q: 1 dy Q.1 Show that the function y = is a solution of the differential equation = 1- dx

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Q: If the differential equation corresponding to the family of curves y = (a + bx) e3x is given by dy =…

A: The given differential equation is d2ydx2=adydx+by....(1) Now, y=a+bxe3x is a solution to the…

Q: 4. Consider the differential equation dy arctan r sin(ry). dx (a) Find all equilibrium solutions.

A: From the given information. The differential equation is as follows.

Q: 4. The differential equation (3.y-4y' +6)dx+(x' – 6x?y' -1)dy = 0is exact because %3D aN

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Q: Given a differential equation xy'+y = (xy) In x with initial an 1 condition y(1)=;. Calculate the…

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Q: How does the following differential equation y dr + x dy = 0 satisfy the criterion for an exact…

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Q: 5. With the substitution cosy == differential equations sin y dy – cosy(1 – x cosy)dx=0 reduced to a…

A: Substitute  cosy=1tNow differentiate it with respect to t,-sinydy=-1t2dtsinydy=1t2dt

Q: 10. What is the integrating factor of the differential equation * y = csc a-ycot a tan a sec x O…

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Q: 4. Solve for the general solution of the differential equation using homogenous equation. [x cos?…

A: A homogeneous differential equation is an equation containing a differentiation and a function, with…

Q: (dr – ()dy = 0 is exact differential equation. zy?

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Q: 44. The integrating factor of the differential equation x dy + y dx x^2 dx is_. 1 O e^-2x O e^-2y…

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Q: 4. 2ydx + (x - a* y³) dy = 0

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Q: 4.Find the particular integral of differential equation (D² +2D)y = 2+x.

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Q: 1.) Obtain the general solution of the differential equation dx – (1 + 2x tany) dy = 0.

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Q: If the integrating factor of the differential equation dy + py = q is sec³ x ,then the value of the…

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Q: y= xtq %3D i a iB a constant yt= In (x-c) ;c iB a unstant

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Q: The appropriate integrating factor for the following differential equation (3xy + y²)dx + (x² +…

A: The given differential equation is 3xy+y2dx+x2+xydy=0....(1) We will find the integrating factor of…

Q: The appropriate integrating factor for the following differential equation (3xy – y?)dx + x(x - y)dy…

A:

Q: 43. The integrating factor of the differential equation (2xy - y^2+y) dx + (3x^2 - 4xy + 3x) = 0 is…

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Q: Q.2 Show that the function y = cos x Fis a solution of the differential equation x +y = - sin x. dx

A: If  y = cos(x)/x is a solution of given differential equation x(dy/dx)+y = -sin(x)     then it will…

Q: 50. The integrating factor of the differential equation x dy + (y - x^2) dx = 0 is.

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Q: +2) dx + (y? Inx) dy = 0, is exact differential equation. Select one: True False

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Q: 5.Given that xsinx is a particular integral of the differential equation y" +y = cosx, the value of…

A: Given DE y"+y=cosx Particular integral y=λxsinx

Q: What is the appropriate integrating factor to the ff. linear differential equation? dy +(1+xcotx) y…

A: Given that, The differential equation is following, xdydx+(1+xcotx)y-x=0 We have to find the…

Q: 4. What is the particular integral for the differential equation D-1) 'y = e*+ 2x-3

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Q: 4. Find the general solution to the differential equation y" + 4y = cos 2x (where y' = ) dx

A: The general solution of a higher-order linear non-homogeneous differential equation is the sum of…

Q: 4. What is the integrating factor of the first-order linear differential equation below? (y – 1) sin…

A: The general form of linear groupntial equation of first order is, dydx+P(x)y=Q(x)

Q: 6. Is the differential equation exact Cos y dx + (y - x sin y ) dy = 0 a) no b) for y3x siny c) yes…

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Q: 20.Find the particular solution of the differential equation x +1) = x3 – 2y, given x = 1 dx when y…

A: We have to find general solution of given differential equation with initial condition.

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…