3y? dy dx cos(пх)" o Consider the differential equation Let y = f(x) be the particular solution to the differential equation with initial condition f (3) = -1. The equation of the line tangent to the graph of f at (3,–1) can be written as y = mx + b. Find b.

Q: 2. What should be A for the exact differential equation of 2.Ay – x y? ry + A , + IP¬ Moreover…

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Q: Find the general solution for differential equation. Verify that  solution satisfies the original…

A: Given differential equation is y2-ydydx=x. Solution: Re-arranging the given differential by…

Q: Consider the differential equation dy = x° (1 – y) with a particular dx solution y = f() having an…

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Q: QI Obtain the particular solution for the following differential equation if y(n) =1 (3x² + ycosx)dx…

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Q: Зx* у + tan y dy Given a first order differential equation dx Q3 x' +xsec? (a) Clarify the exactness…

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Q: 是 Suppose the differential equation = 2x²-1 where y(0) = 0. dx 8) Create a slope field the…

A: To plot the slope field for the differential equation of the form y'(x)=f(x) recall the following…

Q: (30. y4) +y" = 0; 1, x, cos x, sin x, (-, 0)

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Q: Use a computer algebra system to (a) graph the slope field for the differential equation and (b)…

A: Given differential equation is

Q: (3x* – 1)y=x- Zx° †X 2. Find the differential equation of all straight lines at 2- unit distance…

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Q: dy -=x' +y+xy Solve the differential equation dx condition (0) =-1 and 0sxs2 with step length 0.4 by…

A: Given differential equation is, dydx=x2+y+xy With the initial conditions, y0=-1 and 0≤x≤2 We can…

Q: QI Obtain the particular solution for the following differential equation if y(n) = 1 (3x² +…

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Q: a. Verify that the function y = cos x - sinx + x² - 2 is a solution of the given differential…

A: As per the rules we are supposed to answer the first question and rest can be reposted.

Q: Find the general solution of the differential equation y" – y – 2y = cosh(2t). %3D et + e-t NOTE:…

A: Give differentiate equation is y''−y'−2y=cosh2t We have to find the general solution of the given…

Q: Classify the differential equation given below into which type of first order ordinary differential…

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Q: Q3. Second order non-homogeneous ordinary differential equation is given as: y" + y' – 2y = x² –x+e*…

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Q: For an exact equation, Show that this differential equation cos(x+ y)dx= (3y² +2y+ cos(x+ y))cdy = 0…

A: We  are given the differential equation : cos (x+y)dx+(3y2+2y+cos(x+y))dy=0 On comparing with :…

Q: Consider the differential equation 9= 10 -- 2y. Let y = f (x) be the particular solution to the…

A: Given that dydx=10-2y. Let y=f(x) be a particular solution to the differential equation with initial…

Q: Find the function y = f(t) passing through the point (0, 11) with the given differential equation.…

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Q: The elasticity of demand of a service is gìven by E(q) = 1 - (p + 1)+, where E(g) = Dª/ [note that…

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Q: Find the function y = f (t) passing through the point (0, 10) with the given differential equation.…

A: Here Given that,dydt=12tdy=12t dtTaking integration on both side∫dy=12 ∫t…

Q: Solve the differential equation at the given initial value point dy - cos (zx); y(0)=1 %3D dx a.…

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Q: A slope field shows that the slope at the point (1, 1) is 6. Does this slope field represent the…

A: Given yr = 4x +2y

Q: 4. determine the order of the given differential equation; also state whether the equation is linear…

A: d2ydt2+sint+y=sint

Q: Find the general solution for differential equation. Verify that  solution satisfies the original…

A: Given- dydx=y2+16y To Find- The general solution of the above differential equation.

Q: Verify that the general solution satisfies the differential equation. Then find the particular…

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Q: Consider the differential equation 5y with a particular solution y = f(x) dæ having an initial…

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Q: The study of undamped oscillations under the influence of an external force F(t) =F0 cos(ωt) leads…

A: Solution:

Q: (x4cos y) dy + (x + 3x3sin y) dx = 0. Show that this differential equation is not exact. Find the…

A: given  (x + 3x3sin y) dx+(x4cos y) dy= 0 to show differential equation is not exact solution general…

Q: Verify that the general solution satisfies the differential equation. Then find the particular…

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Q: b. Find the most general solution to the associated homogeneous differential equation. Use cj and cz…

A: Here we will have to solve the equation which homogeneous. Therefore we will not take a Particular…

Q: Find the function y = f (t) passing through the point (0, 10) with the given differential equation.…

A: Given: dydt=-9t; y0=10 for finding solution of given differential equation, we use variable…

Q: Consider the differential equation dy dx = x(3+ 2y) with a particular solution y = f(x) having an…

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Q: The differential equation of y = 4c sin x after elimination of the arbitrary constant c is O y =…

A: Given:  y= 4c sinx.

Q: The governing differential equation for a spring-mass system is given below. Initial x (0) = 2 and…

A: The differential equation for damped oscillation is  m·d2xdt2+b·dxdt+k·x=0, or, m·x..+b·x.+k·x=0,…

Q: Q4: Find the general solution of the differential equation y'+ (tan x)y = sec2 x %3D

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Q: The differential equation formed by eliminating arbitrary constants a and b of y = 8 a sin æ + b is…

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Q: particular

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Q: dy cos 2x; y(0) = 1 dx

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Q: (dN/dt)+N=Nte^(t+2) First order differential equation

A: From the given problem:   dNdt+N=Ntet+2   From the variable separable of the differential equation:…

Q: dx Show that a solution of the differential equation is y = (1 + 2x) sin3x Sketch the graph of y(x).

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

Q: Determine the order and degree of the differential equation y' + y" = sinY O 1st order, 4th degree O…

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Q: Find the solution of the differential equation that satisfies the given initial condition. (Remember…

A: Solve the differential equation by separable variable

Q: Verify that the given functions form a set of solutions of the given differential equation on the…

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Q: dy 3x* y+ tan y x'+x sec² y Q3 Given a first order differential equation dx (a) Clarify the…

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Q: Let y = f (z) be the particular solution to the differential equation = -3z'y with initial condition…

A: Consider the differentiate equation dydx=-3x2y3 Here, the objective is to find the equation of the…

Q: Solve the differential equation by variation of parameters. y" + y = sec (0) tan(0) y(0) = C₁cos (0)…

A: Sol:- While solving the question , initial θ is considered as 't' At the end , we will replace t…

Q: a function y= F(x) SatisFying Hhe given find differential equationand the prescribed initial…

A: First we check type of differential equation i.e. Separable differential equation       Homogeneous…

Q: The integrating factor of non-exact differential equation (z'y - 2)dz – (sf –*y)dy -0 1 1

A: With the standard results of integrating factor, we find it.

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.