If we use the method of undetermined coefficients, the particular solution of the following differential equation y(3) + y' = 3 + 2cos (x) has the form Yp(x) = Ax5 + Bx* + Cx³ %3D +Dx cos(x) + Ex sin (x) This option Yp(x) = Ax + Bx cos(x) +Cx sin (x) This option

Q: Suppose that a large mixing tank initially holds 300 gallons of water in which 50 pounds of salt…

A: The brine is entering more and going out less at rate (3 gal/min -2 gal/min = 1 gal/min), so…

Q: By the alimination of the arbitary constants a and b ,obtain the differential equation of which…

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Q: A There is no correct answer from among the given choices. differential equation by separation of…

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Q: The differential equation y'= x – 2xy can be solved by two methods. These are:

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Q: the 2nd order of the non-homogeneous differential equation, y''-y'-6y=4xex using methods of…

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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: It is possible to obtain the particular solution without first obtaining the complementary A…

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Q: The solution of Bernoulli Differential equation y'+-y=3y²; x>0 will be found after reducing it to…

A: Given, The bernoulli's equation y' + yx = 3y-2            x>0

Q: xy '+ y = x²y²lnx (x=1 => y=1) Solve the above differential equation for h = 0.5 in the range [0,2]…

A: Given :  dxdy+y = x2 y2 ln x     dxdy= x2 y2 ln x - y  x=1  y=1 h = 0.5    range [0,2]   To Find…

Q: The universal solution of the differential equation below may be found by substituting y=zx. Hence…

A: Given that                       x2 dydx = y (x+y)   hence we have to find the solution of d.E

Q: Using the method of undetermined coefficients, The general solution of the differential equation y"…

A: Let us consider the differential equation y''+Ay'+By=Q(x) To solve the equation using undetermined…

Q: The equation y" + y'- 2y = x² is called a differential equation because it involves an unknown…

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Q: use the method of variation of parameters to find a particular solution of the given differential…

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Q: The solution of the given differential equation for y(1.5) is h=0.1 interval value. Calculate by…

A: Euler's method uses the formula, yn+1=yn+hf(xn,yn) to perform the iterations.

Q: For this question, please consider the nonlinear partial differential equation ux3 + uy3 = u2.…

A: Given : ux3+uy3=u2 To Find : (i)complete solution                (ii) ux ,0 =x+1327

Q: Find the general solution of xy' + y = y2lnx Bernoulli's differential equation.

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Q: The general solution of an nonHomogeneous Differential Equation using the parameter variation method…

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Q: Determine an appropriate choice for a particular solution for the differential equation y" + 4y = 3…

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Q: The partial differential equation is to solve: XUx + YUy = 0, with U(0,Y)=e-y^2  and i have that the…

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Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

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Q: If we use the method of variation of parameters, the particular solution of the following…

A: I have given solution in step2

Q: If we use the method of variation of parameters, the particular solution of the following…

A: We have to assume the appropriate solution first.

Q: the given differential equation is not exact and hence show that Solve it x²ydx -lx3+y?)dy=0

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Q: Find the particular solution to the differential equation: dy = 3x² cos² y. sSolution passes through…

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Q: The general solution of the homogeneous differential equation 4x'y" + 9xy' + y = 0 can be written as…

A: Solution of the given Differential Equation

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Q: Suppose dr - =4sin(2x) and y= -2 when *=. what is the particular solution to the given differential…

A: In this question, we need to find the particular solution to the given differential equation.

Q: Obtain the general solution of the given differential equation using the appropriate method. y' = y…

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Q: If we use the method of variation of parameters, the particular solution of the following…

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Q: use the method of variation of parameters to find a particular solution of the given differential…

A: To solve the following differential equation using the method of variation of parameters to find the…

Q: on - Homogenous: To be considered Homogenous, the differential equation must be equal to ependent…

A: We are asked to find the  non homogeneous second order euqation.

Q: The particular solution of the differential equation: et y" – 2y' + y =

A: Please see the explanation below

Q: Determine the particular solution of the given differential equation: y = 2(3x +y) – 1. when x-0.…

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Q: The function y = x2 In x is a solution to the differential equation 4x² y" + y = 0. First, use…

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Q: If we use the method of variation of parameters, the particular solution of the following…

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Q: Find the general solution of the first-order differential equation                       y cos x −…

A: Given: y-1cosx+dydx=0 for finding solution of given differential equation, we use variable separable…

Q: ) Find the particular solution of the differential equation dydx=(x−3)e−2ydydx=(x−3)e−2y satisfying…

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Q: Choose a solution for the differential equation y'' - y = x2ex + 5: e-x(1/6x3 - 1/4 x2 + 1/4x + 3)…

A: Given non- homogeneous differential equation,y''-y=x2ex+5  ...(1). Solving the homogeneous part:…

Q: In this problem, we will solve the initial value inhomogeneous differential equation in two steps.…

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Q: What is the general solution with steps of the differential equation y’=sin(3x)y+y+sin(3x)+1

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Q: Find particular solution of the differential equation dydx-2x+13=4x+1y , given x=0, when y=0

A: I have solved using integrating factor

Q: 3. The differential equation = 8 – 2y can be solved using the method of separation of variables or…

A: solve using separation of variable dydt=8-2y dydt=-2y+8 dydt=-2y-4 dyy-4=-2dt take integration…

Q: If we use the method of variation of parameters, the particular solution of the following…

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Q: Find the particular solution to the differential equation: dy/dx=3x^2cos^2y. Solution passes…

A: The given differential equation is in variable separable form. We solve the differential equation by…

Q: Find the particular solution to the differential equation y′ = 4x + 3 passing through the point…

A: To find: y'=4x+3dydx-4x=3       dydx+Py=Qwhere P and Q are variables of x onlyI.F.(Integrating…

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: Solve Bernoulli differential equation of y + ry = ry².

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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.