A nonhomogeneous linear differential equation has the following form: an (x) ym) + an-1 (x) yn-1)+...+a2 (x) y" + a1 (x) y' + ao (x) y = g (x) Determine g (x) in the following equation: y" – y' +3y = 2 cos r +3 sin 2x O 3 sin 2r O 2 cos z +3 sin 2x O 2x O 2 cos z

Q: Consider the first-order differential equation for y(x): dy = y tan x + sin x . dx du find a…

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Q: Identify the exact differential equation. O (1+ y?) dæ + (1 + 2y) dy = 0 %3D O sin 3x da + cos 3x dy…

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Q: The solution of the differential equation 5/1 – x2 ? dy dx 7/1 - y? = 0 is - 5 sin-x – 7 sin-y = C 5…

A: Question is solved.

Q: Find the general solution of the following differential equations: (y² + 3)dx – () ydy = 0 - (cos(x…

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Q: What is the general solution to the differential equation (3 tan x – 2 cos y) sec?x dx + tan x sin y…

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Q: b) Find the regular singular points of the differential equation (x + 2)°(x – 1)y" + 3(x – 1) y'…

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Q: Which of the following is the general solution of the differential equation dy - sin? (2y – x)? dx…

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Q: Determine the order of the following differential equations: xy = 1 y" +x*y' = 2 (b) (y)3 +x 1 (d)…

A: The order of a differential equation is the highest derivative present in it.

Q: t) Are the following differential equations exact? ( 3 dy 3 choose +y= dx - 1. Choose (5y – 2x)y' -…

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Q: 8.) Match the following differential equations with their phase portraits A.) x" + 10x' + 24x = 0…

A: Differential equations as it's phase portraits given below

Q: (b) Given the differential equation (DE) (y? cos r – kay – 2a)dr+ (2y sin r- a* + In y)dy = 0. %3D…

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Q: (a) Solve the following Partial Differential Equation: If f(t) = sin²t, find L(f)

A: We find Laplace transform.

Q: What is the general solution to the differential equation (2xy – tan(y))dx + (x² – xsec?y)dy = 0? |

A: First we have to show that the differential equation is exact. Then we find the general solution of…

Q: Evaluate the given differential equation cosy sin2x dx + ( cos²y – cos x)dy = 0 A. cos x (1+ siny) =…

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Q: 3. Solve the differential equation subject to the given conditions. d² y dx² a) b) d² y dx² +36y= 0,…

A: As you didn't mention the question number to be solved so I solved two questions. For remaining…

Q: Which of the following is a linear differential equation? O sin(x)y' + cos(y) = 3x O y - 2y = In(x)…

A: Given that, There are 4 Differential equations , and we cave to find the Linear Differential…

Q: Solve the differential equation: Cos(x)dx + ( sin(x+y) + sin(x– y))dy=0 Hint: sin (A ± B) =sin A cos…

A: Given differential equation  cos(x) dx + {sin(x+y) + sin(x-y)}dy    Using identity of sin(x+y) and…

Q: 1. dx +y = y² +y = y² (cos x - sin x) dx

A: "Since you have posted multiple questions, We will provide the solution only to the first question…

Q: (a) Solve the first order linear ordinary differential equation dy x sin x- + (sin x + x cos x) y =…

A: The solution is given as

Q: (y cosx+2.xe" ) dx +(sin x + x°e' -1)dy = 0

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Q: Find the general solution of y' =y sec x. A. y = C (secx+ tan x) B. y= C (sec x – tan x) C. y = C…

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Q: Consider the following differential equation. (x - y + y² sin(x)) dx = (6xy5 + 2y cos(x)) dy

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Q: Find the Padé approximation R1.2(x) for f(x) =(ln(1 + 2x))/x

A: Pade approximation R1,2(x) for f(x)=ln(1+2x)x…

Q: Find the solution to the given equations: (a) y" + y' – 2y = cos(x) – 3 sin(2x), y(0) = 1, y'(0) = 2…

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Q: Match the differential equation with its direction field. y' - 8(x + y) - 1 -0.3- -0.2 0.1 0.1 - 0.2…

A: Matching the differential equation with its direction field  y'=8(x+y)-1 x 0 0 0 0 0.1 0.2 0 1/8…

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.