Solve y' + y = f (t) with y(0) = a, where f (t) is shown on pg 577, #37 (sawtooth wave)

Q: The integrating factor of the differential equation as shown is e^(-y).

A: Given that: dxdy+x-y=0

Q: What is the solution to the differential equation if x = 1 at t = 0 and, dx/ dt = 0 at t = O?

A: dxdt=0  at t = 0 means that the slope of normal line passing through the point (1, 0) is 0.

Q: 8. Use a substitution to solve the homogeneous 1st order differential equation (x – y)dx + x dy = 0

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

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Q: Xoly-y dx-Jx.ye dxz0

A: Given:            xdy−ydx−x2+y2dx=0

Q: Show that y = sin−1 x satisfies the differential equation y = sec ywith initial condition y(0) = 0.

A: The given differential equation is y' =  sec y,  with initial conditions y(0) = 0.We want to show…

Q: on) solve the Differential en by using vanation of parameters - 24 (+12 yll -24¹ +y₁

A: Please see the below picture for detailed solution.

Q: Consider the autonomous first-order differential equation dy/dx = y – y° and the initial condition…

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Q: What is the general solution to the differential equation (3 tan x – 2 cos y) sec?x dx + tan x sin y…

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Q: Find the Wronskian of two solutions of the differential equation ty" -t(t-3)y' + (t5)y=0 without…

A: Given differential equation is t2y'' - t(t-3)y' + (t-5)y = 0

Q: y' – y = 2te',

A: Laplace transform: L(y'(t))=py(p)-y(0) L(y(t))=y(p) L(2tet)=2(p-1)2

Q: What is the differential equation obtained by eliminating the parameter A from the relation…

A: The explanation of answer as follows

Q: Verify that y=sinx is a solution to dx dy 2cos x-sin x+y and solve the 2 cosx differential equation…

A: Given Information :  Differential equation : dydx = 2cos2x - sin2x + y22 cosx  y1 = sinx y(0) = -1

Q: Find the values of the constant r so that y = e™* satisfies the differential equation 2y" + y' — у…

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Q: Make the Non exact differential equation xy dx+(3y^2+2x^2−20) dy=0 to an exact differential…

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Q: Provided the integrating factor (IF) = x-2y-2, find the general soution of the differential equation…

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Q: Solve Bernoulli differential equation of y' + xy= ry². %3D

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Q: Prove that the function y = ecos* satisfies the differential equation: y" + sin(x) y' +y cosx = 0

A: Find y' , y" and put into given differentiatial equation.

Q: satisfies the differential equation Show that y = x+ Vx' + dy - m°y = 0 + x- dx

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Q: The differential equation of the family of curves orthogonal to x² + y? = C² is

A: Solve the above questions.

Q: Find the solution of the differential equation tan x dx +tan y dy=0.

A: Here we have to find the solution of the differential equation  tanx dx + tany dy = 0.

Q: Determine the equation of the curve passing through the origin in the from y = f(x) which satisfies…

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Q: equation that satisfies the initial condition(s). f ''(x) = sin(x),    f '(0) =

A: P

Q: Suppose you have the differential equation: y' + p(x)y ln(y) = q(x)y. Prove that the substitution v…

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Q: Consider the first order differential equation f'(t) = dy = f(t, y); y(to) = Yo dt and describe how…

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Q: Show that the solution of the differential equation dy/dx=sin(x+y)+cos(x+y) is  1+tan(x+y)/ 2 =…

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Q: Find the general solution of the differential equation. Use C, C1, C2,⋅ ⋅ ⋅to denote arbitrary…

A: Consider the given differential equation: y'x=4tan2x-3cosx Here, the objective is to find the…

Q: Find the solution to the differential equation that satisfies the given condition. I am having…

A: Given differential equation can be written as Integrating both sides , we get

Q: Find the general solution of the differential equation = 6 tan(5y) using separation of variables. dx…

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Q: Find the curve y that satisfies the differential equation y' sin r and passes through the point (T,…

A: Integrating the equation

Q: 4. Form the first-order differential equation of y = e(sin y + r) %3D

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

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Q: (f) y' – 2y = 1 + 2x – sin(x)

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Q: Explain why the initial Value problem dy/dx=x-cos(y); y(1)=pi has a unique solution. For that…

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Q: Solve the separable differential equation. dy (1+y²) coshx dx 9+sinh x

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Q: The degree and order of the differential equation 1+ is = dy dz о 12, 1 O 1, 15 O 15, 1 O 3, 1

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Q: The integrating factor that transform the differential equation y" +y' + Axy = 0 into a…

A: Given - The differential equation y'' + 1xy' + λxy = 0 To find - The integrating factor that…

Q: (f). Verify if the differential equation given by 10x°y* + e¬Y + 3 sin(4x + 3y))y' + (6x²y° + 4…

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Q: Find the function y: (0.x) → R that satisfies the ordinary differential equation ry'(x) + y(x) = x²…

A: Given : y : 0 , ∞→ℝ   ;  xy'(x)+y(x)=x2 cosx        ;  yπ = 0 To Find : solution of ordinary…

Q: Find the terminal value, lim y (r), for the solution of differential equation dy + 3z'y - 6z". dr

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Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

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Q: What is the integrating factor for the linear differential equation xy' – 2y = x?

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Q: Xoly-yolx- Jrig? dXこ0

A: For checking the function is homogeneous or not , firstly we find dydx and then we calculate the…

Q: Find the solution of the differential equation that satisfiesthe given initial condition.

A: Given: The differential equation y'tanx=a+y with initial condition yπ3=a for 0<x<π2. To find:…

Q: Suppose the motion of a mass-spring system is described by the differential equation x"+By'+1y=0.…

A: We will use knowledge of basic differential calculus to solve this problem.   It should be noted…

Q: Verify if the given functions are solutions of the differential equation. Also, determine the value…

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