Find the values of r for which y = e"* satisfies the equation y +2y -8y=0

Q: Ans: (x + y)e+y = C y'+--2

A: Given differential equation is homogeneous differential equation which can be solved by converting…

Q: Solve for the General Solution of the given first-ordered Lineor DE : X lx² +1)y'+2y= (x?+1) %3D

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Q: Find the particular solution of y2dx+x(x+y)dy=0, when x=1, y=1. Let x=vy.

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Q: y" - 6y' + qy 2,

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Q: Find the formulation of a particular solution of y" + 3y' +2y = 3+t2 – te-2t cost without…

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Q: Differentiate √(xy) + 2x = √y explicitly with respect to x. Show your solution

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Q: Given y = Vx – 2Va – 2; Find y'. - |

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Q: Use the Adam-Bashforth method of the second order to solve the second equation y’=y(x+y) when h=0.1…

A: Given differential equation is y'=y(x+y), step size h=0.1 with initial condition y(0)=1 Let x0=0,…

Q: Use variation of parameters to find the particular solution to 3t y'' + 5y + 4y = 2e Y(t)=| Preview

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Q: utt = 0; x € (-0o; c0), t E [0, o) equation for u(x,0) = at

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Q: Find the general solution for dø = z(z – z²)sec²Ø %3D | dz

A: the given differential equation is: dϕdz=zz-z2sec2ϕ we have to find the general solution of the…

Q: Determine the value(s) of r such that y (t) = e"t is a solution to y" + y' – 6y = 0.

A: Since part B and PART C are independent of PART A question.  As per the guidelines I am answering…

Q: Let y(x) be the solution for the DE: y = (x+y+ 2)2 If y(0) = -2, then find y() %3D

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Q: Use the technique of variation of parameters to find a particular solution to the DE y" – 2y + y =…

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Q: If y In(z- y) then y at the point where y = 0 is equal to

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Q: 7. Eliminate a and b from the equation y =- In(ar +bx) where a,beR-(0}

A: q-7 eliminate a and b from the equation y=12lnax2+bx  this can be written as 2y=lnax2+bx⇒e2y=ax2+bx…

Q: Use variation of parameters to find a particular solution of 14aie" 3 y" – 2y' + y - Yp(x)

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Q: Use Picard's method of successive approximation to solve the equation de 1+ xy, y(0) 1 at 8.1 X-0.1.

A: Given differential equation is  dydx=1+xy, y(0) = 1 To approximate the solution at x = 0.1 using…

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

A: To find the particular solution for the given DE.y''-5y'=x-2, when x=0, y=0, y'=2

Q: Use undetermined coefficients to find the particular solution to y'' – y' – by = 3e* Y,(t) =|

A: The given differential equation is  y"-y'-6y=3e3t  We have to find the particular solution of the…

Q: Find the solution to y - x+t y' = y if r(0) = 5 and y(0) = 4. %3D

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Q: The second order homogeneous Cauchy-Euler equation defined by: 2d²y +bx- dy ォマ +cy=0 dx2 dx (ay"…

A: We have to choose the correct answer

Q: Find general solution to Cauchy-Euler equation: (t^2)y''-2ty'-3y=t^2

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Q: Find the particular solution of y²dx + x(x+y) dy=0., when x=1, y=1. Let x=vy

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Q: wherey = x + C is a solution to this DE. What is the particular solution?

A: Let's find.

Q: Use undetermined coefficients to find the particular solution to y'' – y' – by = 2e-2 Y(t) =

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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: x²y"+xy'-y= x 2

A: Given Cauchy-Euler equation is x2y''+xy'-y=x.

Q: Find a particular solution to æ' = -x – y + e', y' = 2x + y – ešt using undetermined coefficients.

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Q: y" + y = 0, y(0) = 0, y' (5) = 2

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Q: integrate ƒ over the given curve. ƒ(x, y) = x + y, C: x2 + y2 = 4 in the first quadrant from (2, 0)…

A: We have to find the integral The parametric equation of given curve is

Q: 1. y' + 2y = x²y³ .2.3

A: Given problem:- solve the given differential equation y' +2y=x2 y3

Q: 2. In each exercise, obtain the particular of solution. a. xy dx + 2(x² + 2y²) dy = 0; when x = 0, y…

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

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Q: 2 ydx = 3xdy; when x = -2, y = 1 Ans. y = (x/2)3

A: Given: 2ydx=3xdy ; x=-2, y=1   We know that; ∫1ax+bdx=1alnax+b+C

Q: y = x* + 1, y = 0, x = 1 around the ar axis.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 2. In each exercise, obtain the particular of solution. 2y-) dy = 0: when x= 0, y = 1 (3x +v) dy =…

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: Use one step of Euler’s method to approximate y(0.1 + π/4 ) if y′ = xsin(x + y) and y( π/4 ) = 0.

A: Use Euler method

Q: Verify that y = 1/(x+ C) is a solution to y'= -y², where C is some constant. Find the particular…

A: Given that: y=1(x+C)

Q: y +y² – 1 = 0, Yı = 1

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Q: Given x²y3 = In(xy) Show (using complete solution) if the equality below holds dx (x\(3x²y3 – 1) dy…

A: Using differentiation

Q: (b) Find the general solution of: = yx² - xy ax Given z = y when x=1, determine the particular…

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Q: 3. Find the general solutions of, dy_x+y dx х-у, а.

A: given differential equation is  dydx=x+yx-y

Q: use euler's numerical method to obtain an approximation of y (0.6) with h = 0.1 where y(0.2)=1

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Q: Integrate h (x, y. 2) = yzi+xj+xzk over the indicated path: (a) the line segment from (0, 0. 0) to…

A: definite integrate calculus

Q: Determine the solution of y dt + (2yt + I) dy -Ogiven that given that y (-1) = Q

A: 2. We need to determine the solution of the differential…

Q: The longest interval in which the I.V.P y" + (tanx)y-xy x, y(1) = 3, y'(1) = 0 surlay has a solution…

A: Given,  y''+tanx y'-xy=x It is of the form,  y''+p(x) y'+q(x) y=g(x)