Solve the exact differential equation (In y - y sin x-6e)dx + ( + cos x + 5 sec y tan y - 6y)dy = 0 y (A) x In y+y cos x -2ex +5 sec y -3y² = C (В In хy - уcos x - 2e3X-5 sec y -Зу?3D с B) x Inу-усоs x -2е3x+5 tan y - Зу?- с x In y +y cos x-2ex+5 tany – 3y² = C

Q: Solve the differential equation subject to the indicated initial conditions. y" – 2 y' + 5 y = 1+t,…

A: Given differential equation is y''−2y'+5y=1+t and y0=0, y'0=4 We have to solve the given initial…

Q: Consider a nonhomogeneous differential equation y" + 4y = -12x + 10e-*. (a) Verify that yp = -3x +…

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Q: What is the general solution of the differential equation y" +4y= tan 2x? Oy C1 cos 2x + C2 sin 2a -…

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Q: Show that the differential equation  (2xy3 - 3y2 + 2xy2)dx + (3x2y2 - 6xy + 2x2y)dy = 0 is exact and…

A: To show that the differential equation  2xy3-3y2+2xy2dx+3x2y2-6xy+2x2ydy=0 is exact and to find its…

Q: y'= (x²y- y)/(y+1);when x = 3, y = -1

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Q: - (Ax + B) - Ar + B where A = acz and B = bez. When i--a 0, the differential equation becomes X* +…

A: By using relationship between trigonometric, hyperbolic and exponential functions you can solve the…

Q: ind the solution of the Differential Equation: (2y^3 - x^3)dx + 3xy^2 dy=0 ; when x=1, y=1

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Q: Solve the second order differential equation ÿ + 3y = x3 + sin x sinx +글stnx +sinx D: y = c,cosv3x +…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Solve the differential equation. y'+y tan x = cos x, - n/2 < x < r/2 A y = x sin x + c cos x, - 12…

A: Consider the given linear differential equation which is required to solve. Comparing the above…

Q: 1. Verify that for constant C the function ø(x) = + Cx is a solution of the differential equation 2…

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Q: Evaluate the general Solution to the differential equation: Cy-cos-x)dx+ cosxody A y(secx + tan x) t…

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Q: Solve the given third-order differential equation by variation of parameters. y''' − 6y'' − y' + 6y…

A: The given equation can be written as D3-6D2-D+6y=e4x. The auxiliary equation is m3-6m2-m+6=0. Using…

Q: Verify that y1 = x^3 is solution of the differential equation x^2y′′-6xy' +12 y = 0. Using reduction…

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Q: Prove that the differential equation (x2 + 2ye2x) dy + (2xy + 2y2e2x) dx = 0 is exact and find its…

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Q: Determine the solution of the differential equation d5x ,d*x d3x d2x + 12 + 8 - ds5 ds4 ds3 ds2 а. x…

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Q: Obtain the differential equations satisfied by the given puiiicular 3. y = e5x - 3x - x2 4. y = e3x…

A: According to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Often a differential equation with variable coefficients, y" + p(t)y' + q(t)y = 0 (1), can be…

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Q: the differential equation y''+ 9y = sin(3t) + 2 cos(3t), y(0) = 2, y'(0) = 1

A: Given y"+9y=Sin(3t)+2Cos (3t) --1y(0)=2 and y'(0)=1.Auxilliary equation associated to the…

Q: Determine the form of a particular solution to the differential equations. Do not solve. (a) x" – x'…

A: (a) The associated homogeneous differential equation is                     x''-x'-2x=0…

Q: 9. Solve the differential equation (2 sin?y + 4x² sin y)dx + (3x sin y cos y + 2x³ cos y) dy = 0…

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Q: verify that the given equation is a solution of the differential equation.(elimination of Arbitrary…

A: The solution is given as  y=-cos(x) ln(sec(x)+tan(x))                   (1) Differentiate equation…

Q: Determine whether each equation is a solution to the given differential equation. Fully justify your…

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Q: Find a solution for y in terms of x that both satisfies the differential equation and passes through…

A: We have to find the solution of differenrial equation

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

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Q: Suppose that a fourth order differential equation has a solution y=6e^(5x)xsin(x). Find the initial…

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Q: Solve for Linear Differential Equation of Order n: y′′−2y′+y=7e^x+75sin(2x)

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Q: The General solution of differential equation def ined by: 2x² y " – x y'+y=0 is defined by y(x) =…

A: Solving Cauchy Euler differential equation

Q: y^2dx + (x^2 + 3xy + 4y^2)dy = 0; when x = 2 , y = 1

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Q: The solution of variable separable differential equation -1+y* is %3D dx 1+x² a) tan y =tan x+c b)…

A: As per our guidelines I am solving one question. Please resubmit other question.  I am solving…

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

A: Calculation shown in the solution is correct , i am providing you the  answer for each boxes…

Q: what is the solution to the differential equation 2\sqrt(xy)(dy)/(dx)= 1 at y(4)=1

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Q: Verify that the general solution satisfies the differential equation. Then find the particular…

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Q: (y-x)y'=y-x+ 2; y=x+2√√√x+5 When y = x + 2√x + 5, Thus, in terms of x, (y-x)y' = y=x+2= Since the…

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Q: Verify that the general solution satisfies the differential equation. Then find the particular…

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Q: Verify that the general condition satisfies the differential equation. Then find the solution that…

A: y''+9y=0 is the given DE with the general solution y=C1sin(3x)+C2cos(3x)...(1) To verify the general…

Q: 2. Solve the differential equation using undetermined coefficients satisfying the given conditions.…

A: Given differential equation  y"+y'=sin x    ;  y(0) =y'(0) =0 As per our guideline, we are supposed…

Q: 2xy cos(x^2) - 2xy + 1]dx + [sin (x^2) - x^2]dy = 0

A: Note : “Since you have asked multiple question, we will solve the first question for you. To get…

Q: The solution of the differential equation (xy – y²)dx – (x² + y²)dy = 0 is : %3D A) 2 In + 1| – In |…

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Q: Find the particular solution of the differential equation y’ + 7x = 0, at y = 0, x = 3. y = 63x2/2 y…

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Q: I. Determine whether the given differential equations are homogenous or not homogenous. If the…

A: NOTE : as per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly repost…

Q: Verify that the expression: 1 C(t,T) = 1 e-b(T-t) 1 + ab -a(T-t) a(a – b) b(a – b) is the solution…

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Q: Verify that the indicated function y = p(x) is an explicit solution of the given first-order…

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Q: Often a differential equation with variable coefficients, y" + p(t)y' + q(t)y = 0 (i), can be…

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Q: What is the general solution for the differential equation y" + y' = cos x + 4e¯*? A. y = Cx +…

A: Solution:

Q: Verify that the function   ...    is a solution  of the  differential  equation x dy/dx+3y=2x5 and…

A: Given,          xdydx+3y=2x5

Q: Obtain the solution to the differential equation: (cos'x- cos'y ]dx+ cosx sin 2ydy = 0 a. cos"y(1+…

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Q: Find the general solution of the differential equation or state that the differential equation is…

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Q: The General solution of differential equation defined by: x2 y"-2x y'-4y=0 is defined by 1 y(x) = C,…

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Q: The particular solution of the differential equation y y- 2y = sin3x is: y(x) =Ce3x+Ce3O…

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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.