Show that the function: y = -xcos (x) – x is a solution to the differential equation: dy :) = y + x² sin(æ).

Q: Find the implicit general solution to the differential equation. 2xy3 + e* + (3x²y² + sin y)y' = 0…

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Q: If the characteristic equation of the differential equation dy dy + y = 0 has two equal + 20 dx2 dx…

A: Quadratic Equation: A quadratic equation is an equation of degree 2. The standard form of a…

Q: Verify that the function is a solution of the differential equation.

A: Given ,differential equation is:y''+y=0 Given function is: y=C1sinx-C2cosx Differentiating both…

Q: Solve the first order differential equation dy ycos' x 1+ sin x dx

A: The given equation is first order, linear differential equation.

Q: Verify that the function y = x sin(x) + x cos(x) is a solution to the differential equation: y" + y…

A: 1 have verified the differential equation by finding each derivatives

Q: Determine whether the function y = 2 sin 2x is a solution of the differential equation y"-8y = 0.

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Q: Determine whether the function y = x2 ex + sin x + cos x is a solution of the differential equation…

A: Here given function as y = x2 ex + sin x + cos x .....(1)

Q: The indicial equation for the differential equation 2xy" + y + xy = 0 is 2c² - 1 = 0. True False

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Q: Determine whether or not y=C1 cos (2t) + C2 sin (2t) is the solution to the differential equation…

A: we check y=c1 cos(2t)+c2sin92t) is the solution to the differential equation y''+4y=0

Q: Solve the non-Linear differential equation cOS y dy = sin y(1 – O sin y).given that y(0) = 4.

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Q: Find the solution of the differential equation y"+y'= sin x y = C, + C2 e¯* – sinx +co a. - b. y =…

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Q: of the differential equation x' = 4 sin 2t, which (c) x(π/4) = 2. = 2

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Q: e. Cxy +C'x + 9 = 0

A: Cxy+C2x+9=0

Q: Let y=A cos x + B sinx is the solution of the differential equation

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Q: y cos x dx+dy=0 y

A: Given query is to find the solution of the differential equation.

Q: Obtain the differential equation associated with the given primitive, A and B being arbitrary…

A: y=sinx+A y=sinxcosA+cosxsinA

Q: Prove that the function y = ecos* satisfies the differential equation: y" + sin(x) y' +y cosx = 0

A: Find y' , y" and put into given differentiatial equation.

Q: Determine whether the function y = 3 cos x is a solution of the differential equation y(4) − 16y =…

A: y=3cosx and the differential equation is y4-16y=0. Consider, y=3cosx Differentiating with respect to…

Q: Find the solution of the differential equation tan x dx +tan y dy=0.

A: Here we have to find the solution of the differential equation  tanx dx + tany dy = 0.

Q: Find the solution to the differential equation below such that y(0) = 8 y' = 8xy – 2x y(æ) =

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Q: sin y(x + sin y)dx + 2x cos ydy = 0

A: Given: sinyx+sinydx+2x2cosy dy=0Bernoulli's equation:dydx+pxy=qxynLet v=y1-nLinear differential…

Q: 1 (c) y' + 2kxy? = 0, y(x) = %3D 1+ kx?

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Q: Give the differential equation that has as its general solution. y = C₁ sin(2x + C₂)

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Q: Find the implicit solution of the differential equation (1+sin(y))dx + (1+x cos(y))dy = 0.

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Q: If the function y = A sin z + B cos a satisfies the differential equation y" + y – 2y = sin z for…

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Q: Solve the Euler Cauchy differential equation d²y x2. dx2 dy +y32(Inx) dx -

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Q: Obtain the differential equation. y = e*(C, cosx + C2 sin x)

A: Given that : To form an differential equation of the given functiony=ex (C1cos x+C2sin x)Formulae:*…

Q: Assume that y is a function of x and use the integrating factor method to solve the differential…

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Q: Find the solution to the differential equation below such that y(0) = 8 y' = 8xy – 2x - y(x) =

A: Given: y'=8xy-2x    , y(0)=8 Taking y'=8xy-2x ⇒y'-8xy=-2x To make calculation easy multiply both…

Q: (b)Verify that the differential equation y = 2 sin 2x is a solution y" + 4y = 0

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Q: Verify that the function y = C1 sin x − C2 cos x is a solution of the differential equation y″ + y =…

A: The given function is y=C1sinx-C2cosx. Obtain the derivative of the function as follows:…

Q: The solution of the exact differential equation (²+y' cos x)de+ (2xy+3y sinx)dy=0 is:

A: The given equation is y2+y3cos xdx+2xy+3y2sin xdy=0 The given equation is of the form Mdx+Ndy=0…

Q: Find the general solution of the differential equation. Use C, C1, C2,⋅ ⋅ ⋅to denote arbitrary…

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Q: Solve the fourth order differential equation completely d*y d°(y/x) dx sin(x)+ cos(x) %3D 3 dx³

A: Given: A fourth order differential equation…

Q: Show that the differential equation dy / dx = y / x is inexact and that a factor of 1 / x ^ 2 can…

A: Given differential equation is, dydx=yx.

Q: Find all solutions to the differential equation. Use c to denote an arbitrary constant. y' = x ln(x)…

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Q: Verify that the function y = a cosx + b sinx where a,b e R is a solution of the differential…

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Q: Find the I.F of this nonexact differential equation dy/dx=1/(2xy)

A: Please see the answer below.

Q: Find the general implicit solution to the differential equation xy2 cos(x)dx + 2xy sin(x)dy = 0.

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Q: Find the general solution of the differential equation y' + y = te-t + et and use it to determine…

A: The differential equation is given as

Q: Solve this first order differential equation dy, 2 +y = -x²y? cos x

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Q: Solve the non-Linear differential equation dy Cos y de sin y(1 – 0 sin y),given that y(0) = 8.

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Q: What is the general solution to the differential equation sin y (x + sin y)dx + 2x² cos y dy = 0 ?

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Q: Determine whether the given differential equation is separable. dy + 10 sin (x - y) = 0 dx

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Q: Solve the differential equation as follows: (6xy* – sin x tan y)dx + (12x²y³ + sec? y cos x – 5y²)dy…

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Q: Solve the differential equation dy/dx = 4 sin 2x ; y = 2, when x = π/2

A: Given: dydx=4 sin 2x Also given that x=π2…

Q: Show that the function y=e−2x(sin3x+cos3x) is a solution of the differential equation y′′+4y′+13y=0.

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Q: (d) y' = x(1 + y²), y=tan(\x²)

A: Solution of the differential equation satisfy  the differential equation

Q: Solve the fourth order differential equation completely d*y d°(y/x) - = sin(x)+cos(x) dx* dx³

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