Find the general solution of the Cauchy-Euler equation: X^3y’’’ - x^2y’’ + 2xy’ - 2y = x^3

Q: Give the solution of the initial value problem of the Cauchy Euler Equation. If it is not possible…

A: Given differential equation is t2d2ydt2−7tdydt+5y=t2−2.......1 and y1=2,dydt1=1 Let t=ez Then…

Q: find the genecol solution of Cauchy EuLer equation

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Q: 3. Determine a homogeneous linear equation with real, constant coefficients that is satisfied by: y…

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Q: Find the product solutions for the differential equation ux = -3uyy using separat of variable…

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Q: Show that the following differential equations are homogenous and solve

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Q: Integrate: ∫sec^(3)2xdx

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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: Is this polynomial, x In x – y In y - a homogeneous differential equation?

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Q: 3. Determine a homogeneous linear equation with real, constant coefficients that is satisfied by: y…

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Q: Solve by Chain Rule y = tan ( V3x² + In(5X*))

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Q: Find a differential equation that corresponds to the given direction field.

A: This is a problem of slope field.

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: Find the differential operator which will annihilate the function 2x + r³ – sin 2r.

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Q: Write the smallest differential operator that annihilates the given 3x +x²e + sin(5x) e3 sin…

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Q: 2 Express the flowing equation in Cartesian equationr = 1-cos e

A: The given polar equation is: r=21-cosθ

Q: xdx S- can be solved by either algebraic subsitution or integrataion by parts. Vx-1

A: We have to find the following integral

Q: 3) Find the solution af equation that satisties the qiven mitial condition. of the differential L0…

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Q: When I am solving an integration question, how should I know which expression to equate to 'u' in…

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Q: Suppose m1 =4 , m2 = -5, m3= -2 are roots of multiplicity one, two and three of an auxiliary…

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Q: The differential equation ry" + 3y - 7y=seca is normal on any open interval not containing a = 0.…

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Q: Find all the solutions of partial differential equation 25u ôx? by variable separable %3D method.…

A: All the solution of the partial differentilal equation is(1) u(x,t) =(Ax+B)(Ct+D)    (2)…

Q: Obtain the particular solution of (3siny-5x)dx+2x^2cotydy=0 using Bernoulli's Equation. (Complete…

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Q: Find a differential operator that annihilates 4e2" cos 3x + 3x²e5.

A: Let L be the differential differential operator that annihilates 4e2xcos3x+3x2e5x. Find L.

Q: solve for the differential eq   (8x−10xy+4y^2sin^2 (x) )dx=(2ysin2x+5x^2−4xy)dy

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Q: Find the general solution of the inhomogeneous equation y" + 3y' = te'.

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Q: Use a linear approximation (or differentials) to estimate the given number.   27.tan 2°

A: The Linear approximation of the function at x=a is given by L(x)=f(a)+f'(a)(x-a) To Find Linear…

Q: x²y' + 2xy = In x, У(1) 3D 2

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

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Q: (1-) ex, 4. S ex 2dx

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Q: 5) Form a DE by eliminating the arbitrary constants from the equation y = asin(4x + 1).

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Q: Solve MXVN at (1,1-1) When M = (2yz)i – (x²y)j + (xz²)k and N = 2x²yz³ Show the graph after it.

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Q: Find a differential equation whose general solution is y = ciet + cze-4t. %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: Find a homogeneous Euler-Cauchy differential equation whose general solution is Cx1+ C2x? where C,…

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Q: Solve the nonhomogeneous opdr – 2rdo = q' In odo. equation

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

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Q: Suppose sinh 2x, y2 = 6x, y3 = cos 2x are solutions of a linear homogeneous differential equation…

A: To find the differential equation :-

Q: ly 3)[e^(-2y)]dy

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

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Q: Solve the differential eguation 3-

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Q: Find the general solution to the DE using the method of Variation of Parameters: у" — Зу" + Зу' — у…

A: The solution is given as

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: A flexible stretched string is constrained to move with zero slope at one end x=0, while the other…

A: Given: A flexible stretched string is constrained to move with zero slope at one end x=0, while the…

Q: Obtain the differential Equation from the family of ellipses centered at (h.k) whose semi-major axis…

A: Here h,k are parameters ,not constant.

Q: 2. Solve cosx +3- 2x = 0, correct to three decimal places by using fixed point iteration method. %3D

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Q: using partial differential equ

A: Charpit's auxiliary differential eqs are

Q: Find atleast three approximations of a solution of the equation f(x) = x – 2x = 0 by Newton Rampson…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: find all solution of z   sinh(2z)=-1

A: Consider the provided equation, sinh2z=-1 Find all solution of z. Apply the trigonometric…