If a nonhomogeneous linear differential equation has g (a) = sin 5a, what is the form of its particular solution? O A sin Br O A sin 5a O A cos 5a+ B sin 5a O 5 sin Ar

Q: find the general solution of the first-order linear differential equation. y' + (tan x)y = cos x

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Q: For which values of n is the function ya solution of the differential equation xy"-Kxy'-6y=0

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Q: Write a fifth-order differential equation that has the following general solution: Cез* + Сzе-2х +…

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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: When solving the nonhomogeneous differential equation y" - 4y' + 4y = x by undetermined coefficients…

A: To solve the following problem

Q: Given the differential equation: D'(sin x- cos x+3e" +x) What is the second derivative? a - sin…

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Q: An ordinary differential equation of a horizontal string which is freely pinned at both ends is…

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

Q: State the order of the given ordinary differential equation. (sin 8)y"" - (cos 8)y' = 7 Determine…

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Q: The value of 'a' for the exact differential equation (1+ +)dz - dy is O - 4 O 2 O -2

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Q: 6. (D² + 1) y = x cos x

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Q: 3. If the general solution to a second-order differential equation is given by cie + ce-5, find the…

A: In the question it is asked to solve the differential equations with initial values given.

Q: sin x sin y y' cos x cos y

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Q: show that there exists a unique solution to the differential equation y'=ln(xy); y(2)=1  the…

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Q: 4.Determine if the given function is a solution of the given differential equation

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Q: I. dy tan(x) dx Cos (x) + x²

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Q: The equation, sin y-2 sin(2) sin(2y) y+ cos z + 2acos () cos(2y) = 0 is an exact differential…

A: We have to solve

Q: Bernoulli Equation xydx+ (x ?-3yJdy

A: Given xy dx +x2-3ydy=0xy+x2-3ydydx=0xy+x2-3yy'=0

Q: 4. y = x cos(In x) x²y" - xy + 2y = 0

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Q: The equation, sin y- 2 sin(2) sin(2y) y+ cos z+2xcos (z) cos(2y) = 0 is an exact differential…

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Q: The Solution of the differential equation g + 9y= -6 cos (3x) – 30 sin(3x) initial conditions…

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Q: An ordinary differential equation of a horizontal string which is freely pinned at both ends is…

A: Given problem is :

Q: Given the differential equation: D°(sin x-cosx+3e* +x) 1. What is the second derivative? a - sin…

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Q: what is the particular solution to the differential equation dy/dx=3sin(x)(2-y)with the initial…

A: You need to apply variable separable metod to solve the given differential equation.

Q: 1.) Find the general solution to the first order differential equation given below. -3x 3xe 2x y' 4y

A: In the given question we have to solve the given ordinary differential equation of first order and…

Q: What is the general solution of the first order differential equation a csc (2) - B| da + a dß = 0…

A: Given that first order diffrancial equation is αcosecβα-βdα+αdβ=0  function α=fβsolution…

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: If a nonhomogeneous linear differential equation has g (x) = sin 5a particular solution? O A sin Br…

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Q: Show that the differential equation (- y² – y sin r + x²)dx + ( cos x – 2xy – 2021y²) dy = 0, | is…

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Q: If the auxiliary equation of a differential equation of order 2 has roots r1 =7 and r2 = 7, then the…

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Q: e. xy' – y = x*y"

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Q: sin(ax)y = -a cos(a.x)y + a

A: Given that  The differential equation  To find the general solution

Q: (メyーx+24 -2) dx- (x+ 4x) 0

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

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Q: The objective of this question is to identify the solution of the non-homogenous Ordinary…

A: There is a typo in the ODE given. The expression in the RHS should be        2a-12ea Given :…

Q: 6. If y = x (In x), find d²y / dx².

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Q: An ordinary differential equation of a horizontal string which is freely pinned at both en is given…

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Q: The solution of the following homogenous differential equation y' = - x+y -is

A: We find the solution of the homogeneous differential equation y'=yx+y

Q: 13) The linear differential equation whose general solution is given by x = Aet + Btet + cos(3t)…

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Q: Solve the given Cauchy-Euler differential equation. For problems with initial values, plot the graph…

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Q: y = C1e2" sen(x)+ C2e²" cos(x) +x² + C3x + C4.

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Q: 4. When solving an auxiliary equation of a certain differential equation the roots m = 1 ± 2j are…

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

Q: Determine whether the differential equation (cos(y°) – 2xy+ 2)dx – (5xy*sin(y³) + x²)dy is exact. If…

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Q: In the equation (ax+by+c)dx + (ex+fy+g)dx = 0, if b=e, then the equation is said to be exact…

A: A differential equation of the form Mdx+Ndy=0 is said to be exact differential equation if it…

Q: (D² + 1) y = x cos x

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Q: 5. The Bernoulli's form of the differential equation xdy-[y + xy ³ (1 + ln x)]dx = 0 is In

A: Given xdy-y+xy3(1+lnx)dx=0

Q: The particular solution of the following nonhomogeneous differential equation y" – 2y' +y = x² + e¬*…

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Q: )(I + cos x) y Sin?x + Sin? x cos x -y sinx

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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: Given the linear differential equation: y'' - y = cos(x) - 5sin(2x) Find the general solution…

A: Solving

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.