Particular Integral for the differential equation (D² + 25)y =(cos5x) is given by a. -xsin5x 5 b. xcos5x 10 c. -xsin5x 10 d. xsin5x 10

Q: An Integration factor of this differential equation is .7 3x? + 1 + x3 dy 1 y : 1+ x2 dx

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Q: SOLVE FOR EXACT DE DIFFERENTIAL EQUATION 3. (x + 3)cos ydx - [siny In(5x + 15) - y] dy = 0

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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: 2. Form a Differential Equation for the given equation y = 2 cosx + 5 sinx by eliminating the…

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Q: Solve the partial differential differential by separation of variables 70z + 6 = 0.

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Q: Find the general solution of the first-order linear differential equation. y + y = 16 cos (x)…

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Q: Find the differential equation by eliminating the arbitrary constant/s. 1. y¹= x(2e + c) 2. y = Ae³x…

A: 1. y-1=x2ex+c Note:     Multiple questions are given, we are answer with only one question. If you…

Q: Find the particular solution of the differential equation = 10y sin(x) using the given boundary…

A: To find the particular solution of the given differential equations

Q: The order of the differential equation of all circles of given radius a is: 3 2

A: Let's find.

Q: Obtain a linear differential equation with real, constant coefficients that is satisfied 1 sin 2 1…

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Q: Find a particular solution of the differential equation COS X dy dx 1 +ytanx = cos x e cos x for…

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Q: Form the differential equation whose primitive is given by y= ex(a cos⁡x + b sin⁡x),  a, b, being…

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Q: Since dv = cos( cos9 x) dx, integrate the differential equation to obtain the function v. V = ^p -…

A: We have to find solution

Q: [cos y + 1]dy + [tanx (siny + y)]dx = [sin y cos x + y cos x]°dx gettyimages When:x = 0;y=

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Q: ду 9. The differential equation (3ycos.x+4xe" +2x'e" dx+3(sin x+1)dy 0 is exact because ON 10. The…

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Q: Consider the differential equation y"+ya+x. If g(x) is a solution of the differential equation…

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Q: Let y = 4x. Find all values of r such that y = rx satisfies the differential equation. If there is…

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Q: Find the particular solution of differential equation = 4ye* using the given boundary condition: y =…

A: We have differential equations and both of them are variable separables.

Q: 5. The differential equation (3x'e' - 2xx+ (r'e' -sin y ldy = 0 is exact because ON

A: Partial differentiation is needed to be done after identifying M and N

Q: Solve the differential equation by variation of parameters. y"+y = n²(x) xx) = c₂cos(x) + csin(x) +…

A: The solution is given as

Q: 21. Find particular solution of the differential equation- 2(x + 1)³ = dx (x+1) Y , given x = 0,…

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Q: Q1 By eliminating the constants A and B from the equation y = Asin 2x + B cos2x, form an ordinary…

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Q: A nomal is drawn at a point P(x, y) of a curve, it meets the x-axis at Q. If PQ is of constant…

A: Equation of normal at the point P(x,y) to the curve is Y-y=-dxdy(X-x). ⇒X=x+ydydx Thus,…

Q: Q19// Solve the partial differential equation du = Iny sin-x given that дхду = cosx when y-0 and u=y…

A: Initial value problem are those problem in partial differential equation in which initial condition…

Q: 2. Find the differential equations by eliminating the arbitrary constants of a) y = C₁x + 2² b) y ex…

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Q: Use separation of variables to solve the differential equation explicitly for u. du dt = 4 + 4u + t…

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Q: a differential equation is classified as a homogeneous DE if one can directly isolate all functions…

A: A differential equation is classified as a homogeneous DE if one can directly isolate all functions…

Q: 4. y" +2y'+ = cos a COS

A: We will solve the problem

Q: -ka dt2 Sdlve the differential equation and express the X func tion of trieonometrie func tion as

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

A: Topic:- application of integration

Q: 15. x" + x = tan t; x=-(cost) In(sect + tant)

A: Given, x''+x=tant x=-costlnsec(t)+tan(t)x''=cos(t) ln(tan(t)+sec(t))+tan(t)

Q: Q2 Form a differential equation from the function y = (4– 2 cos x) x)cosx.

A: Given below the detailed solution

Q: Find the general solution of the differential equation y + 18xy* = 0 using separation of variables.…

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Q: Find the particular solution of differential equation 3ye" using the given boundary condition: y = 2…

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Q: The differential equation obtained by eliminating the arbitrary constants A and B from the relation…

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Q: Find the differential equation by eliminating the arbitrary constant/s. 1. ecosx = c(1-cosy)-¹

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: The solution of the differential equation using variable separable 4/1- y². O sin y = 4x +e O cos 'y…

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Q: Form the differential equation whose solution is y = c1cosz + c2sinx Also find the particular…

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

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Q: Show that the differential equation [y(1+1/x)+cosy]dx+[x+lnx-xsiny]dy=0 is exact.Hence solve it

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Q: The solution of the differential equation by variable separable method dy (1+ y²) (3x² + 6) 5- is dx…

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Q: ,Find the two values of k for which y(x) = ekx is a solution of the differential equation %3D…

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Q: 13. Obtain the differential equation of the family of straight lines at a fixed distance p from

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Q: Verify that the indicated function is an explicit solution of the given differential equation.…

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Q: 3. (sin'x + cosv)dx - tanxsin2ydy = 0

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Q: The given differential equation is already in standard form, as the coefficient of the highest order…

A: We have to find Wronskians.  Wronskian W(y1, y2) is the  W(y1, y2) = y1y2' − y2y1' Since y1 and y2…

Q: 3x√y. For y is not

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Q: From the differential equation by eliminating the arbitary constants A and B from the equation…

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Q: dx + dt? dx +x = 2 dt x, dt6 dt3 = of this differential equation is 9, help (numbers) tion is Choose

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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.