The salution of the differential equation dy subject to the boundary conditions ylo) = 1 and y(0)=0 is %3D as Cost + sint C> Cos hlt) + sinhlt) b> Cost - sint d) Cosh(t) - sinhlt)

Q: Show that ¢(x) = Ce³* + 1 is a solution to dy/dx – 3y = -3 for any choice of the constant C. Thus,…

A: We have to check Q(x)=Ce3x+1 is solution of given differential equation.

Q: Given the differential equation of the family of circles with radius of 2 units and whose center's…

A: The equation of a circle is x-a2+y-b2=r2. Here, the center is a, b and radius is r. The abscissa is…

Q: Using the substitutions 2= sin y and dz=cos y dy, the differential equation (3sin y – 5x)dx +2x² cot…

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Q: What is the integrating factor for the linear differential equation 2(y - 4x^2) dx + x dy = 0?.

A: Given:  2(y - 4x^2) dx + x dy = 0

Q: Consider the differential equation y' = x+ y. Use Euler's method with Ax = 0.1 to estimate y when x…

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Q: Show that the solution, of the differential 5x3 is of у — ху? — х*у dy equation: dx xy² – x²y – 2r³…

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Q: 2. Show that these differential equations are exact, then integrate to find the solution. (a) dy +y…

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Q: Given the differential equation of the family of circles with radius of 2 units and whose center's…

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Q: Make the Non exact differential equation xy dx+(3y^2+2x^2−20) dy=0 to an exact differential…

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Q: Provided the integrating factor (IF) = x-2y-2, find the general soution of the differential equation…

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Q: The solution for the differential equation (D2 + X²)y = 0 with boundary conditions y(0) = 0, y(3) =…

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Q: Find a suitable integrating factor to solve the first the first order linear differential equation…

A: Y(X)= x2+x

Q: 1 of these 2 differential equations: dx dy O and (2x sin y +y) dx + (x² cos y + x)dy = 0 What are…

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Q: 2. (cos x cos y cot x) dx + (- sinx sin y) dy = 0

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Q: Make the Nonexact differential equation xy dx+(3y^2+2x^2−20) dy=0 to an exact differential equation.…

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Q: At any particular time, the rate of change at which the vertical position of an object moving in…

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Q: Find out all the curves passing through (0,-1) satisfying the dy 1( dy dx 4 dx differential…

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Q: Suppose that every constant multiple of a solution is also a solution for a first-order differential…

A: It is given that the differential equation dydt=ft,y, where ft,y is continuous on ty plane. Suppose…

Q: Use separation of variables to find the general implicit solution to the differential equation. 4…

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Q: The integrating factor for the differential equation dy X- dx 4x cos(x)y = –5e* is e-4 sin(x) Select…

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Q: dy Show that given differential equation da y cos z + sin y + y sin a + r cos y +x 0 is Exact and…

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Q: Using the substitutions 2- sin y and dz- cos y dy, the differential equation (3sin y - 5x)dx +2x cot…

A: The solution is given as

Q: (y') ² + (x-2x^-½) y'+ x^-1 - x^½= 0

A: As per the company rule, we are supposed to solve one problem. Therefore kindly repost the second…

Q: -) Solve the following partial differential equation us ing direct integration: a²u = cos (x +y) дх…

A: Topic:- application of integration

Q: In this problem we consider an equation in differential form M dx + N dy = 0. The equation (6x +…

A: First we will make the given differential equation exact by calculating the integrating factor then…

Q: A population (in thousands) grows according to the differential equation dy e ky(L-y), where the…

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Q: 2. y" + 4y' + 5y = cos(x)

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Q: Show that (2x cos y + z siny) dx + (xz cos y – x² siny) dy + x siny dz is an exact differential.…

A: Given differential equation,2x cos y z sin y dx + xz cos y -x2 siny dy + x sin y dz =0

Q: By using variation of parameters, what is a possible value for u'1 for the differential equation y''…

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Q: The integrating factor of the differential equation (x+x sin 2y) dy =2y dx js: A x-3

A: We will find the integrating factor as shown below

Q: The transversality condition holds for the partial differential equation X4x +Uy=0 with the initial…

A: In the given question we have to check the transversality  condition of the given P.D.E s.t xux+uy=0…

Q: 6. Given that y = 0 when x = 1, show that the solution of the differential dy equation 2xy- - = y² +…

A: Answer and explanation is given below....

Q: Match the differential equation with its direction field. y'- sin(10x) sin(10y) 20) -0.3 1-0.2 1…

A: Remark: We know that the slope field is a graphical representation of a differential equation. This…

Q: Suppose that a fourth order differential equation has a solution u Se sin(r) a) Find such a…

A: For the solution of differential equation y=8xe4xsinx the auxiliary equation will have solution: 4+i…

Q: If the integrating factor of the differential equation dy + py = q is sec³ x ,then the value of the…

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Q: Using the substitutions 2 = In y and dz= - dy , the differential equation xtan x + In y)dx +tan x…

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Q: For x € 0,, What is the particular solution of the differential equation (y + ysinx)y' = /cos?x –…

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Q: The integrating factor that transform the differential equation y" +y' + Axy = 0 into a…

A: Given - The differential equation y'' + 1xy' + λxy = 0 To find - The integrating factor that…

Q: he of the curves corresponding to different values of C in the general solution of the differential…

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Q: What is the general solution to the differential equation (tan x)dy – (4y In y – y tan³x)sec²x dx =…

A: Given differential equation:(tanx)dy-(4ylny-ytan3x)sec2xdx=0To find: General solution of the…

Q: The differential equation dy 4e" cos(y) + 3 dr 4e* sin(y) – 6y In(x) + 3y? Has solutions of form…

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Q: What is the simplest form of the integrating factor for the differential equation y' +…

A: Given: The differential equation is y'+2sec xy=cos2x. To find: The correct option for the…

Q: Evaluate the curve f(x, y) = 0 which passes through the point (0,4) and satisfies the differential…

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Q: The Particular Integral of the differential equation (D² – 9)y = 6 cos 3x is PI = 6 sin 3x 18 O PI =…

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Q: The reduced form of the given Bernoulli's dy dx + 3xy = 4xy³ to differential equation the Linear…

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Q: Is the differential equation y sin 4x dx + x cos 9y dy = 0 exact? %3D Choose the most appropriate…

A: A Diffrentaial equation in the form :-  M( x, y)dx + N(x, y) dy = 0 is an exact  if,   ∂M/∂y =…

Q: What is the general solution to the differential equation (tan x)dy – (4y In y – y tan³x)sec²x dx =…

A: We will convert given differential equation into linear differential equation by appropriate…