Use eigenfunction expantion methodto solve: у 1 d -(xy'). dx y(1) = e, y(e) =0 : x x

Q: Solve the partial differential equation of Lagrange’s form y^2 zp-x^2 zq=x^2 y.

A: We will solve the pde using lagrange's auxiliary equations.

Q: How Three Functions of Wronskian are used to Find the Homogeneous Linear Differential Equation Whose…

A: Let's consider two function y1(x) and y2(x) are the linearly independent solution of y'' + p(x) y' +…

Q: Fromthe partial differential equation by elimaniting the arbitary function ø, and ø, from z= 0 (x…

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Q: a²u(x, t) at² a²u(x,t) (-∞ 0 ) əx² и (х,0) — 4е-5)x] initial conditions ди -(х,0) %3D 0 at

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Q: Suppose !=sinh2r, z= 6ư, 3s= cos2r are solutions of a linear homogeneous differential equation with…

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Q: Use the initial condition to find the particular solution of the differential equation. Differential…

A: We have to find

Q: Form the partial differential equation by elimaniting the constants form z=axey+1/2 a2e2y+b

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Q: State the order of the partial differential equation uxx + Uy = u + 4. Then classify whether it is…

A: We are given the following partial differential equations uxx+uy=u+4. The order of the PDE is 2.…

Q: A car traveling at 100 km/h skids 50 m after its brakes are suddenly applied. Set up a differential…

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Q: The roots of an auxiliary cubic equation are m1=-1 and m2=m3=-5. What is the corresponding…

A: We have given the roots of an auxiliary cubic equation ,  m1 = -1  , m2 = m3 = -5 Thus , Auxiliary…

Q: Make a phase diagram indicating whether the critical points correspond to an attractor or a repeller…

A: We need to create a phase diagram (slope diagram) and analyse its behaviour at the critical point.

Q: Classify the partial differential equation ´ôx² ôyôx ôy²

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Q: Consider the differential equation I+y Using isoclines, construct a direction field, maybe even plot…

A: Given: y'=x-yx+y

Q: 3. (x – 3)²y" + 3(x – 3)y' + y = 0, x > 3

A: Cauchy differential equation

Q: USE EXACT DIFFERENTIAL EQUATIONS To SOLUE THE $OLLOWING: In dx-tn(x=2) 'पर्क - डेण बर =0 y dy dx 3D0…

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Q: form the partial differential equation by eliminating the arbitrary function from z=xy+f(x2+y2)

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Q: Form the partial differential equation by eliminating the arbitary function from z = xy + f(x² +y°)

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Q: O Classify the partial differential equation which represents parabolic or hyperbolic or elliptic:…

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Q: 1 y" + 3 y + 2 y 1+ et

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Q: Suppose that the differential equation x' = Ax is such that A is a 2 x 2 matrix with (G) (-)…

A: Here, the eigen values are: λ1=5λ2=3

Q: Use eigenfunction expantion methodto solve: d y 1 -(xy')- dx y(1) = e, y(e) =0 : %3D

A: Given, ddxxy'-yx=1xxy''+y'-yx=1xx2y''+xy-y=1....1 Let, x=et then, x2y''=θθ-1yWhere, θ=ddt then,xy'=θ…

Q: Find the solution of the partial differential equation- = 3 dt? by variable separable method

A: given partial differential equation  ∂2z∂x2=3∂2z∂t2 to find -solution of the partial differential…

Q: Use a computer algebra system to graph the slope field for the differential equation and graph the…

A: The differential equation is dydx=0.8y, y(0)=4. Solve the equation as follows.…

Q: Sketch the direction field of the differential equation y'=cos(xy); trace a solution through the…

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Q: Classify the partial differential equation which represents parabolic or hyperbolic or elliptic: =…

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Q: Eliminate the arbitrary constants from z= (x-a)^2 + ( y- b)^2 to form the partial differential…

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Q: Form the partial differential equation from z ax + by + ab by eliminating the constants

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Q: dx 5 dt dy 3 dt

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Q: /y' + 10 = 0, y(0) = 2 and y'(0) = 4 %3D %3D

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Q: State the order of the partial differential equation -3uxx = 5uy + 10u + 5. Then classify whether it…

A: Given the partial differential equation is -3uxx = 5uy + 10u + 5 ⇒ 3uxx + 5uy + 10u + 5 = 0…

Q: State the order of the partial differential equation uxx + uy = u + 4. Then classify whether it is…

A: The order of the highest derivative term in the equation is called the order of the PDE.

Q: Find a partial differential equation by eliminating a, b, c Iro

A: To eliminate the constants a,b,c in the equation we will partially differentiate the equation with…

Q: Solve the partial differential equation of Lagrange's form  xy2p-y3q=-axz.

A: P p+ Q q=R z We solve partial differential equation by method of Lagrange's multiplier The…

Q: The formation of the partial differential equation by eliminating arbitrary constants a, b from the…

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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: Consider the nonlinear time-dependent ordinary differential equation (ODE) y '(t) = y ^2 (t)+…

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Q: 3] Form the partial differential equation by eliminating arbitrary function from z = e® f(x – y) -

A: Given: Z=exfx-y

Q: Suppose that the differential equation x' = Ax is such that A is a 2 x 2 matrix with eigenvalues A1…

A: Draw the phase potrait : Draw the eigen vectors corresponding to eigen values and corresponding…

Q: Solve the system of ordinary differential equations defined by dx/dt+y = cost dy/dt+x = −sint

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Q: The formation of the partial differential equation by eliminating arbitrary constants a, b from the…

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Q: Obtain the solution of the partial differential equation with initial conditions using the Fourier…

A: Given: d^u(x, t)/dt^2 = 9 d^2u(x,t)/dx^2    (-∞< x < ∞, t>0)   u(x, t)=4e^(-5|x|) du/dt(x,…

Q: Classify the partial differential equation +34 = sin(3x + 4y).

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Q: Find the eigenfunction assuming the second case for the given boundary value problem. y" +ly = 0…

A: The given problem is to solve the given boundary value problem y"+λy=0, with the given boundary…

Q: Classify the partial differential equation uxx-2 sinx uxy - cos^2x uxy- cosx uy=0

A: Given Partial differential equation is  uxx-2 sinx uxy - cos^2x uxy- cosx uy=0

Q: Form the second-order differential equation using the parametric definition of y = asin0, x = acos0

A: Calculate dydθ and dxdθ first. Then calculate dydx, d2ydx2 and simplify to get the differential…

Q: Solve the partial differential equation Obtain using the Fourier transform with initial conditions.

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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.