Identify the exact differential equation. O (1+ y?) dæ + (1 + 2y) dy = 0 %3D O sin 3x da + cos 3x dy = 0 O (y4-y sin x) de + (4xy + 3y2 cos r) dy = 0 %3D O (y² + ya) dx + a²dy = 0

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

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Q: 01- Solve the differential equation:(answer any two question) y. (a)(e* + In y +2)dx+(+Inx+sin y)dy…

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Q: Find all singular points for the differential equation (x³+25 x)y"+sin(x) y'-x² Y3D0 { 0,4 i, - 4 i}…

A: Consider the given differential equation, x3+25xy''+sinxy'-x2y=0 the general second-order ordinary…

Q: State the order of the given ordinary differential equation. d?u du dr2 + u = cos(r + u) dr…

A: (1).  The given differential equation is: d2udr2+dudr+u=cos(r+u)

Q: The differential equation formed by eliminating A and B from y = e-2* (A cos x +B sin x) is A. y2 -…

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Q: Form the differential equation for the function y = a sin3x -bcos3x O a. y" - 9y 0 O b. 9y" + y = 0…

A: Given differential equation is: y=asin3x-bcos3x                                                (1)…

Q: (a) Find the general solution of the differential equation (2xy +3y)dx (2ry + x²)dy = 0. (b).…

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Q: Solve the differential equation, 2ydy = (3y? cot r +sin rcosr) da sin z- sin 3* y² = C %3D csc z csc…

A: We will find out the required solution

Q: Solve the differential equation e sin 2y dx - 3x-cos 2y dy A - 3ln(sin 2y) = C B +3 In(cos 2y) = C…

A: .

Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

A: The given differential equation is x-y5+y2sinxdx-5xy4+2ycosxdy=0 where M=x-y5+y2sinx,N=5xy4+2ycosx.…

Q: Solve the differential equation y"-3y'-4y 0 O y= e3* (c cos 2x + C2 sin 2x) cos 3x + c2 sin 3x) O y=…

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Q: Solve the differential equation x²y"+ 4xy'+ 2y = 0 %3D اخترأحد الخيارات y(x) = C1a-1+ C2x O %3D y(x)…

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Q: Solve the differential equation. dy 3x?cos? y dx %3D O y = tan-1 (x³3 + C) O y = tan1 (x² + C) O y =…

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Q: State the order of the given ordinary differential equation. (1 – x)y" – 7xy' + 5y = cos(x)…

A: Order of differential equation: The order of the highest order derivative involved in a differential…

Q: estion 7: Find the general solution of the following differential equations. a) y cos(x2) y' cos(x2)…

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Q: Which one of the following is an Exact Differential equation.? (2xy+ sin a²) dx + (x² + sin y) dy =…

A: The condition for a differential equation to be an exact differential equation of the form…

Q: Solve the differential equation: (2+2y) = 2e*y dx In y+2y? = 4e*+c %3D Iny +e* = (1+x²) +c In y + 1…

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Q: Determine the solution of the differential equation y" - 2y' + y = 14 y = C,e + C,xe" +e* In(1 + x)…

A: First we find complimentary function then find particular integral then solution.

Q: xydy – (y² – 3a2) dx = 0

A: As we know that; The expression for the integrating factor of the differential equation Mdx+Ndy=0:…

Q: Solve the differential equation, 2ydy = (3y² cot r +sin xcos1) dr %3D sin z sin 3* y? = C O csc z…

A: We will find out the required solution.

Q: Solve the differential equation [x a. b. C. d. y tan ¹()] 2x tan-¹(²) -¹ (²/2) dx + x tan¯¹ (²/2)dy…

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Q: wo linearly independent solutions of the differential equation y"-4 y=0 are O y,=e** and y, = e 4x…

A: I am attaching image so that you understand each and every step.

Q: Find the value of k so that the given differential equation is exact. (³+kxy-2x) dx + (3xy² +…

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Q: Solve the differential equation:cosx dx +[sin(x+y) + sin(x– y)]dy=0 (A csc?x+ 2siny=C B csc?x+…

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Q: Form the differential equation for the function xy = ae2x – be-2x a. xy" – y' = - 4xy O b. xy" – 2y'…

A: The given equation is xy=ae2x-be-2x. Evaluate the differential equation as follows.…

Q: Consider the differential equation (10x*y4 +e-y + 3 sin(4x + 3y))y' + (6x²y³ + 4sin(4x + 3y) + 2) =…

A: Exact differential equations

Q: solve the differential equation. 1.e-x dy + (e-xy - 4x) dx = 0 2. (x + 3y2) dy + y dx = 0 (Hint:…

A: Consider the provided differential equation,

Q: Given the differential equation (2D2 – 3D+ 1) y = csc(2ra) - Propose an appropriate particular…

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Q: Given the differential equation (2D² – 3D+1) y = csc(2rx) Propose an appropriate particular…

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Q: Form the differential equation for the function x +2y = a sin3x - bcos3x а. Зу" - 18у %3D -9х O b.…

A: The second order differential equation for a function can be found by differentiating the function…

Q: The auxiliary equation of a non-homogeneous differential equation has complex and distinct roots.…

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Q: A solution to the partial differential equation a?u = 9 əx² ay2 a) cos(3x — у) b) x2 + y2 c)…

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Q: solve the differential equation: 2xy dy dx x² + y² +1 Select one: y? 1 O a. F(x,y)=x-++c 1 O b.…

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Q: 1. State the order of the given ordinary differential equation. Determine whether the equation is…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Consider the differential equation: 1 1+e¯* What is the general solution? y" – 3y' + 2y = : Oy = [c…

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Q: Obtain a linear differential equation with real, constant coefficients that is satisfied by the…

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Q: The differential equation y" + ay" + by" + cy + dy = 0 %3D has a solution y = -5te 3t + 3e 3t…

A: Given differential equation y''''+ay'''+by''+cy'+dy=0has a solution y= -5t e-3t+3e-3tcos(4t)

Q: Form the differential equation for the function 2x-y-asin(2x-b) O a. y"+y=x O b. y" +8y = 4x O…

A: Given, 2x-y=asin(2x-b)

Q: Given the differential equation у" — у' — 12у %3D 7ез^ cos(x) Determine the Wronskian for the…

A: Solving wronskian

Q: The solution of the differential equation x1+y dx+y1+x² dy = 0is: %3! Select one: O A. sinx+sin -1…

A: We will solve the following.

Q: Solve the differential equation: (9 + 2x sin y) dx x? cos y dy = 0 O z sin y = ca – 3 O (E) O z +…

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Q: State the order of the given ordinary differential equation. (1-x)y" - 9xy' + 2y = cos x Determine…

A: Order of the differential Equation :  The highest order of the differential Equation is called the…

Q: Solve the differential equation cos(x) y? dy dx by the method of separating the variables. .A y =…

A: The given differential equation is                                             dydx=cos(x)y2…

Q: State the order of the given ordinary differential equation. (1-x)y" - 3xy' + 6y = cos x Determine…

A: Order = highest derivative order = 2

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

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Q: Solve the differential equation xdy]=0 xdx +sin? (%) [yde 4x ln || - 2y + x sin ( ² ) = 0 2x a. 2y…

A: Given :   xdx+sin2yxydx-xdy=0

Q: What is the general solution to the differential equation x = y + y³ cos x ? dx = -2x?(y* sin x +…

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Q: Consider the differential equation: y" + y = sec x,0 <x <n/2 What is the particular solution y.? Yp…

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Q: Solve the differential equation (x' + y' )dx + (3xy² + cos(y))dy = 0 Select one: O a. x + y°x –…

A: e have to find the solution of the Differential equation…

Q: The Pl of differential equation (D²+1)y = sin 2x is %3D a) sin 2x b) sin x c) cos 2x d) sin 2x c) d)…

A: Given: D2+1y=sin2x. We know for particular integral (P.I) of 1fD2sinax, put D2=-a2 provided if…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.