23. (f + 1)dv/dt + 2tv =-1

Q: Find the general solution of thedifferential equation. (2+x)y'=3y

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Q: 3. Solve the particular solution (D² + 3D + 5)y = 5e¬*sin2x using D- operator method.

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Q: Solve Cauchy-Euler equation. a2y"-2y 2x %3D

A: (1) The equation is, x2y''-2y=2x Take y=xm Then take the derivative, y'=mxm-1 Take the derivative…

Q: Explain particular solution of the forced system                     x'' = Ax + F0 cos wt

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Q: y(4) + 3y" + 2y = 0

A: We have to solve given differential equation.

Q: 3. Obtain two linearly independent solutions valid near the origin: 3xy" +(2-x)y' - 2y = 0

A: As per the question we are given the following second order ODE : 3xy’’ + (2-x)y’ - 2y = 0 And we…

Q: Solve for the value of constant(C) by obtaining the orthogonal trajectory of the given equation…

A: As 2 Question are given , I will solve only one: We are given: 8y=b sinx----(1)⇒8y''=b cos…

Q: Compute the solution of the IVP Sz(t) = (sin f)z(t) + sin t, l-(4) = 1, using the method for linear…

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Q: 1 Oy' = %3D xsiny+2sin2y

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Q: y" - 5y' = x - 2, when x = 0, y = 0, y' = 2

A: We have to solve the given differential equation.

Q: By using linear method, solve dy %3D

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Q: 2²y" - 4.xy+6y= 0, y(2)=0, y'(2) = 4 %3D

A: The differential equation is given as x2y''-4xy'+6y=0x2D2y-4xDy+6y=0x2D2-4xD+6y=0 It is a Cauchy…

Q: Find the general solution of the given aifferential equation. Give the largest interval Iover which…

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Q: Q5. Write the governing equation of 1-D heat transfer with convective heat loss and indicate all the…

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Q: Y, = Ax² is particular solution of y' + y" = 1 for A = %3D

A: Here, yp=Ax2yp'=2Axyp''=2Ayp'''=0

Q: 2 b. y" + y' - 2y = %3D

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Q: Use the separation of variables method to solve 4UTr H Utt: 00 uz (0, t) = uz (2, t) = 0 u(x,0) = x,…

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Q: 22 To solve y =cy - by' change to u= 1/y?. Substitute for y in um - 2yly³ to find a linear equation…

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Q: Define Equilibrium solutions (For autonomous equations)?

A: Equilibrium solutions : An autonomous system or autonomous differential equation is a system of…

Q: у" — у' — х %3D 0

A: We are given: y'''-y'-x=0⇒y'''-y'=x Auxiliary equation is : m3-m=0⇒m(m2-1)=0⇒m=0, 1, -1 Hence,  CF=…

Q: Consider the vectors x1 (c) What conclusion can be drawn about the coefficients in the system of…

A: Given vector is, X1=t22tX2=etet Part(c): In case of linearly independent vectors X1 and X2. The co…

Q: dr = -4rt whent=0, r=r, dt Obtain the particular solution of - %3D

A: we have to use separation of variable

Q: 1- , L, v² e*dydx 2- S S マーーー ydxdzdy a>0

A: Explanation of the solution is given below...

Q: 3 Solve dx₁ de dx2 dt = the 2x1 1 following 5x2 -cost x12x2 + sint system. a) by using the method…

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Q: Determine the point of intersection (roots) of the following equations below at 3rd iteration using…

A: As per the question we are given a nonlinear system of equations in variables x,y,z; and we have to…

Q: Use Euler's method to approximate the solution to y' = 2ty – 2 , y(-1) = 2 on the interval [-1, 1]…

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Q: dz (D² + 16)³(D² + 4D – 5)²(D² + 2D – 3)4z = 0, Dz = dx

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Q: Obtain the general solution valid near the origin: 2y'+9ху'-36у 30

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Q: The solution interval of 2y +1≥3 or 3y1 or y< -11 BO

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Q: 1. Find the root of system of equations using Newton Method. Employ initial guesses of x=y=1.2…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Consider the nonlinear system of equations 22 – 3y = 4, 4x – y = 4. (2,-4), one step of Newton's…

A: f1=x2-3y-4=0f2=-y2+4x-4=0 J1,1=∂f1∂x=2x    J1,2=∂f1∂y=-3J2,1=∂f2∂x=4      J2,2=∂f2∂y=-2y…

Q: Solve for the 2nd order nonhomogeneous linear equation: y"+12y'+37y=10e-4t     ; y(0)=4,  y'(0)=0

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Q: apply gauss jordan method to solve the equations x+y+z = 9 , 2x-3y+4z = 13, 3x+4y+5z = 40 plz fast

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Q: 14. dQ/dt + (2/10 + 2t)Q = 4 2(5 + t)² + C 5+t

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Q: Obtain the homogeneous linear equation satisfied by the following function.

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Q: Determine three linearly independent solutions to the equation y" + 2y" – 3y = 0 of the form y(x) =…

A: The given differential equation is                                                y'''+2y''-3y'=0

Q: cos X + cos t e' sin t, X' 1

A: Here is the solution of the given system of differential equations by using Method of Variation of…

Q: y +y² – 1 = 0, Yı = 1

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Q: Solve the non-homogeneous DE. Hint: Use method of undetermined coefficients. y(4) – y = 5; y(0) =…

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Q: Find the particular solution determined by the initial condition. ds 17t +7t-6, s(0)= 86 dt %3D The…

A: The given differential equation is ; ds/dt = 17t2+7t-6, s(0)=86

Q: x' = -2x +y x(0) = -2 y(0) = 2 %3D y' = -5x + 4y %3D

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Q: Recast the system of higher order differential equations as a first order system. u""=2u-3v…

A: The given higher order differential equations are: u'''=2u-3vv''=3tu'v'-cos u Recast the system as a…

Q: Find a solution for y' = y - y, y(0) = 0.2, h = 0.1 %3D using Modified Euler's Method. Hint: do 5…

A: Given that, y'=y-y2, y0=0.2, h=0.1

Q: How to solve this equation y'''-4y''+2y'-8y=6e^(x) - x^(2) + 1 using Laplace Tranformation. Initial…

A: Consider the given initial value problem as y'''-4y''+2y'-8y=6ex-x2+1 with y0=y'0=y''0=0. Apply…

Q: Monster truck Alpha pulls on an object with a force of 12000 N at a direction of [N 15°E). Monster…

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Q: = -y² + 2x²y + 2x – xª, y1 = x² %3D

A: The Riccati equation is of the form

Q: Explain why an equation Ax = b has a solution if and only if b is orthogonal to all solutions of the…

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Q: Determine the roots of the simultaneous nonlinear equations (x – 4)2 + (y – 4)² = 5 x² + y? = 16 Use…

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Q: A certain vibrating system satisfies the equation u" + yu' + u = 0. Find the value of the damping…

A: In this question, The second-order differential equation is given. u''+γu'+u=0 To find the damping…

Q: (D³ + 2D² - 5D - 8)y = 0, when x = 0, y = 0, y = 0, y" = 2

A: Given