Solve the following initial value problem y" + 4y = 8 8(t – 27); y(0) = 3, y'(0) = 0 . %3D

Q: Find the particular solution for initial value problem.

A: x2dydx-yx=0⇒x2dydx=yx⇒dyy=xx2 dx⇒dyy=x12·x-2 dx⇒dyy=x-32 dx Now integrating on both sides, we get…

Q: Suppose a 1000L tank contains 400 L of fresh water at time t = 0. At that time, a salt water…

A: The solution of above question is written below.

Q: If we use the method of variation of parameters, the particular solution of the following…

A:

Q: A population is modeled by the differential equation dP = 1.005P1- dt P 7500 For what value(s) of P…

A: The Given Differential equation is: dPdt = 1.005P1-P7500

Q: Find the particular solution of the differential equation √x + √y y′ = 0 that satisfies the initial…

A: x+y y'=0x+ydydx=0ydydx=-xydy=-xdx

Q: Find the general solution to the separable differential equation: (2x + 1)(x + 1)y' = - %3D For full…

A:

Q: When a capacitor of capacity C is being charged through a resistance R by a battery which supplies a…

A: Given: RdQdt + QC=E The given equation can be written as dQdt +QC=ER

Q: 3. What is the difference between a solution of a differentialequation and a solution of an…

A: The solution represents a family of solutions all of which satisfy the system of differential…

Q: Suppose that a quantity y = y(t) increases at a rate that is proportional to the square of the…

A: Given that a quantity y=y(t) increases at a rate that is proportional to the square of the amount…

Q: ex 2. y" — 2у' + у %3 1+ x2

A:

Q: What integral equation is equivalent to the initial value problem y′ = ƒ(x), y(x0) = y0?

A: Write y'= dy/dxThen separate the variables.

Q: What is the particular solution to the 2² +3 with the differential equation dy da 3y initial…

A:

Q: 10x – 8yva? +1 fip dx 2 = 0.

A:

Q: If we use the method of variation of parameters, the particular solution of the following…

A: We have to assume the particular solution first.

Q: solve the Initial Value Problem. y'= tan y, y(ln 2) = π/2

A:

Q: The differential equation dy/dx = y(y+6) has initial condition of y(0) = 3 What is y(1)? Multiple…

A: Given

Q: 4. Solve the differential delay equation 1 (t) – T2(t – 1) = 1, for any valuе т.

A: given differential delay equation x't-rxt-1=1 for any value of r claim- solve the differential…

Q: If we use the method of variation of parameters, the particular solution of the following…

A: I have given solution in step2

Q: What is the solution of the initial – value problem = x dx with y(0) = 1. and y'(0) = –2 ?

A: This is a problem of IVP.

Q: SOLVE FOR THE PARTICULAR SOLUTION of the differential equation: dy a yax (1+) where a and b are…

A:

Q: 1. Solve the initial value problem dx - x* (1+ y) = 0, y(0) = 5.

A: Explanation: Given that,  dydx-x6(1+y)=0, y(0) Now,  dydx=x6(1+y)1(1+y)dy=x6dx

Q: 3x + y + z = 0; z(0) = −1

A:

Q: Use variation of parameters to solve the given initial-value problem. x'=(³₁3¹)x+ (4²).X (0) = (¹)…

A:

Q: What is the particular solution to the differential equation dy/dx=xy2 with initial condition y(2) =…

A: To find the particular solution

Q: Lake Taal has a volume of 458 cubic km, and its rate of inflow and outflov are both 175 cubic…

A:

Q: 5. Find the solution of the differential equation using Variation of Parameters. у" - Зу" + Зу 3 E

A: Given y'''-3y''+3y'=exx

Q: The differential equation dudx=5u+10  admits one equilbrium solution that is    asymptotically…

A: The given solution is  unstable whose plot is shown below.

Q: 2 Solvehe initial value problems below. dy dt

A: The general solution of a differential equation always contains a constant of integration. The…

Q: Solve the initial value problems dy/dt = et sin (et - 2) , y (ln 2) = 0

A: Given: dydt=etsinet-2

Q: Solve the initial value problem y" – y = cos(x) with y(0) = 0 and y (0) = 1.

A: Given differential equation is y'' - y = cos(x) with y(0) = 0  and  y'(0) = 1

Q: Solve the initial value problem (x² + 4)- dy + 3xy = x, y(0) = 1. dx

A: Given the differential equation,  (x2+4)dydx+ 3xy = x , y(0) = 1 (x2+4)dydx+ 3xy=x(x2+4)dydx=x -…

Q: Use a technique of integration or a substitution to find an explicit solution of the given…

A: To find the solution of the differential equation we use the method of separation of variables. We…

Q: Find the linear, nonhomogeneous differential equation with constant coefficients whose solution is y…

A: We have to find homogeneous differential equation first.

Q: What is the particular solution to the differential equation [x+(1+x)y] = 12 with y = 0 and =0 when…

A:

Q: Solve the differential equation with the given initial condition. y' = y – e2ty4, y(0) = 1

A:

Q: Find the value of the arbitrary constant of the particular solution of the differential equation…

A:

Q: Solve the initial value problem - zy, y(0)-0.35502805. (0) 0.25881940 --

A:

Q: If we use the method of variation of parameters, the particular solution of the following…

A:

Q: The Integrating Factor of the differential equation dy dr y = 14x? is x-14 25 e5z

A: The given differential equation is,  dydx-5xy=14x2To find its integrating factor.

Q: Suppose a population P(t) satisfies logistic differential equation dP/dt=0.1P(1-(P/2000))…

A: SOLUTION-

Q: 3. Solve the initial value problem of y(-1) = 0 dx x+3

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Given y" + (y)° + 5 = 0 is a differential equation with degree 3 and order 5 O TRUE O FALSE

A: Topic = Differential equation FALSE

Q: A tank contains 50-liters of brine in which 20 grams of salt is dissolved. Pure water is being…

A:

Q: 3. Find the particular solution to the differential equation (y + 5)(x+2) if the %3D dx solution…

A:

Q: The population y(t) of a certain microorganism grows continuously and quadrupling time is found to…

A: In this question, the concept of the derivative is applied. Derivative We can use a derivative to…

Q: ev dy Solve the initial value problem given by y(1) = 2. %3D dx y

A: Differential equation: A differential equation is an equation which involves one or more derivatives…

Q: Solve the initial value problem dy y = 5e" + 28e5* dx with y(0) = 8.

A: The solution of differential equation is given as follows :

Q: What is the particular solution of the differential equation (x+y) dx + (x - y) dy = 0 when x = 0…

A:

Q: solve the inhomogeneous initial value problem x = (; ) × (4 ln t X + 1 -2 X(1) = (1). %3D

A: Given,              X˙=2-41-2X+ 4lnt1t,     X(1) = 1-1                        (1)

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.