Question If we use the method of undetermined coefficients, the particular solution of the following differential equation y() +y" 2x sin (x) has the form (x) = (Ax² + Bx)cos(x) Yp(x) = Ax + Bx + Cx +(Cx? + Dx) sin (x) +Dx cos(x) + Ex sin (x) This option This option Yp(x) = Ax + Bx cos(x) +Cx sin (x) Yp(x) - Ax + Bx² + Dx cos(x) +Ex sin (x) This option This option

Q: (1) The functions f, g and h are related by f(x) = g(x+1),. g'(x) = h(x-1), then f"(2x) equals: (a)…

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: Find the general solution of y" + y = 1 3+ sin² t

A: We have a differential equationWe have to find the general solution.For this we find the particular…

Q: Show that if P(x) #0 the differential equation y' + p(x)y = f(x) is not exact differential equation.…

A: y' + p(x)y = f(x) can be written in the appropriate form dydx + p(x)y = f(x)  ⇒dy +p(x)y dx = f(x)…

Q: fnom © we get Now 2 ( yeosx +22ed) dz + (Sinx + xtet +2 ) dy ze on, (yeosz da + Sinz dy) + (2xe%dx +…

A: Okay I am explaining.

Q: Date (2) (3 x² + y cusx) dx + (sin x - 4y³) dy so solve using exact equations X = 0 y = 2 Answer: 0=…

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Q: (x +3) y (prime) + 5y 6 sin x x > - 4 9 (x+3)*

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Q: How do I show that for the differential equation: u''(x) + 6u'(x) + 5u(x) = 10x + 2 x → c1e-x +…

A: The given differential equation is; u''(x) + 6u'(x) + 5 u( x) = 10x + 2

Q: Show that the given function is a solution of the differential equation. y" + 25y = 0, y = cos(5x) +…

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Q: Using variation of parameters, solve the differential equation y" + 3y + 2y = sin(e*). (Hint: [ e²*…

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Q: Given the differential equation y"+y=cse²(x) O A particular solution is given by x − În|csc (x) −…

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Q: (y – x)(y + x)(y? +x²)(xdy – ydx) = x°dx

A: We will solve this homogenous differential equation by a substitution y=vx So v=y/x

Q: Solve using an appropriate method on First Order Differential Equation. Show complete and detailed…

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Q: Solve the differential equation y' + y == A) y= Inx +cx-² B) y= Inx +cx-1 C) y= In x+cx-2 D) y= Inx…

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Q: b. Write down the equation describing the solution's limiting behaviour as t → ∞.

A: If Q is a function of the variable t, when the input t changes, the output Q also changes. If the…

Q: The solution of the differential equation tan xdx + tan ydy = 0 is

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Q: Verify that the indicated expression is an implicit solution of the given differential equation. 1 (…

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Q: Using a suitable substitution method solve the differential equation dy/dx=(4x+y+1)^2

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Q: Find the solution the initial value problem x' -13 X, %3D 1 -3 (1) x(0) cos(3 t) – 4 sin(3 t) x = e…

A: The given initial value problem is…

Q: Use suitable substitution to solve the following differential equations: dy (a) dx = (x + y + 1)² –…

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Q: Problem 2: Pure-time differential equation} \ Consider the following equation d 3t e de (t). +…

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Q: If we use the method of undetermined coefficients, the particular solution of the following…

A: Using variation of parameter we know the standard form of the given particular solution.

Q: If a 4th order linear differential equation is such that the corresponding characteristic equation…

A: If a 4th-order linear differential equation is such that the corresponding characteristic equation…

Q: Q/Find the general Solution to the differential equation Using the transaction method is not…

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Q: please show step by step

A: a. b. c.

Q: Please Explain how to get particular solution

A: The particular solution isy=31​e3t+e4t[8cos(4t)+4sin(4t))]Explanation:Step 1:

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.