16. х" — 7x'— 51 — 3.

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: (4) Form the differential equation by eliminating the arbitrary constants a and b from y=ae +be¯ª.

A:

Q: yu Solve the above differential Equation y making tab lo and deri vatives to' compare fco-efticients

A:

Q: 20. x" +4x = 3e2"

A: We have to solve the differential equation using the method of undeterminedcoefficients and no…

Q: For which values of n is the function ya solution of the differential equation xy"-Kxy'-6y=0

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Q: Use undetermined coefficients to solve the differential equation y"" -y=e¹- x + 16.

A: We have given a differential equation ,  y''' - y = ex -x + 16 First we will find complementary…

Q: Determine whether the equation is exact. If it is exact, find the solution. If the differential…

A:

Q: $2. x" – 4x' +3x =te".

A: Given that x''-4x'+3x=tet To find the general solution :

Q: ScouMARY "+FR'-XR=D0 GCauchy-Euler Diff EQ

A:

Q: 3. Find the general solution y = Yc + Yp to the differential equation. Use the uppercase letters C…

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Q: 4. x"+4x' +4x =0.

A: Let, x = emt be a trial solution. So, x' = memt  &, x" = m²emt So, the characteristic equation…

Q: 3xy dy (In y)8 da

A:

Q: D4 − 1)y = 0 -

A: Topic:- solution of differential equations

Q: Solve for the particular solution of the non-homogeneous differential equation. 1. y''=4

A: Solution :--

Q: By using suitable method, form an ordinary differential equation by eliminating constant A from the…

A:

Q: Determine an appropriate substitution and then solve the differential equation. ху'%3D у In(ху)

A: We will substitute v = xy to solve the given differential equation. after substitution the…

Q: Eliminate the arbitrary constants: y= x+ Ce2x + C2e¬x 1.

A:

Q: 1 Solve the differential equation 2 2zy' with the initial condition y (1) = 1.

A: The given differential equation is,1y2-2x=2xy'y3having the initial condition y(1)=1

Q: (4) Form the differential equation by eliminating the arbitrary constants a and b from y = a sin x…

A: Eliminating arbitrary constants a & b using derivatives.

Q: Solve the differential equation xyª) +6 y" = 0. ,(4) First convert this equation to a Cauchy-Euler…

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Q: 4.Determine if the given function is a solution of the given differential equation

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Q: (x² + y²)dx – xydy = 0 %3D -

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Q: Determine whether the equation is exact. If it is exact, find the solution. If the differential…

A:

Q: y"- by! + gy = e

A: We have to solve the differential equation…

Q: 11. у" - у" - у +у%3D0

A:

Q: Solve the differential equation for y if (1+9x²) dx %3D

A: Here we have to solve the differential equations,  1+9x2dydx=1.................................(1)

Q: 5) Solve the differential equation with appropriate method. xdy-ydx-√(x2 + y2) dx=0   Show…

A: We have to solve the differential equation xdy-ydx-x2-y2dx=0.

Q: 3. x? = Axy + By: A and B are arbitrary constants

A: Given: x2=Axy+By, where A and B are arbitrary constants.

Q: Solve the Bernoulli differential equation with the given initial condition.

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Q: (1) When sugar is dissolved in water, the amount A that remains undissolved after t minutes…

A: We have to find the time taken for half of sugar to dissolve.

Q: The following ordinary differential equation is given, where y = y(x) x 5 2 x y' +- -- 3 = 0 At x =…

A: The backward euler's method for y'=fx,y is yn+1=yn+hfxn+1,yn+1,  xn+1=xn+h.  (a) Given y'+x2-5x-3=0.…

Q: A zircon sample contains 4000 atoms of the radioactive element 235U. Given that 235U has a half‐life…

A: Given- A zircon sample contains 4000 atoms of the radioactive element 235U and 235U has a half‐life…

Q: Solve the differential equation using only methods taught in class. y' + 3xe' = 0

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Q: If the differential equation is = ye", where x = 0, y = e. Determine the value of y when x = 1.…

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Q: Eliminate the arbitrary constants in the equation defined by y = ae^(3x) + bxe^(3x). Which of the…

A:

Q: 2.Form the differential equation from the family of curves y² = Ae³* + Be* , where A and B are…

A:

Q: Vyy" – 1 = y'

A: Given DE is  √(yy''-1) = y'' ......(1)

Q: A cypress beam found in the tomb of Sneferu in Egypt contained 55% of the radioactive carbon-14…

A:

Q: a) Find the differential equation of X ae(2+last digit of your id)y + %3D be-(2+last digit of your…

A: Consider the provided question, Given, last digit of id is 9. Substitute this value in the given…

Q: x" – 5x'+4x =17 sin t+3e.

A:

Q: Solve the differential equation y Pemer 6a y5 subject to the condition that y 3 when = 3.

A: Here we have to solve the given differential equation

Q: II. Solve for the differential equations and get the general solution. Simplify your answer free…

A:

Q: Determine whether the equation is exact. If it is exact, find the solution. If the differential…

A: We have to determine that the given differential equation is exact or not. If it is exact then we…

Q: 4. x" +x=e+!.

A:

Q: 3) Find the solution of the differential equation y = -ry + (/')².

A: The given differential equation is. y=-xy'+y'2                                .........1 This can be…

Q: Obtain the Differential Equation of all circles passing through the origin and (0,8).

A:

Q: 30. x" + 10x =0.

A: We have to find General Solution of the given Differential equation.

Q: If we use the method of undetermined coefficients, the particular solution of the following…

A: y(5)+y(3)=x+cos(x) Particular solution : As equivalent function containing x so (To maximum order to…

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.