(1) y'(t) = 1- sint – , y(t)dt, y(0) = 0 %3D

Q: What is the general solution to the differential equation (tan x)dy - (4y In y - y tan³x)sec²x dx =…

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Q: Find the differential equation of (y cos x + 2xe^y )dx + (sin x + x²e^y) dy =0

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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: (x3 + ) dx + (y² + In x) dy = 0, is exact differential equation.

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Q: Assume that the rate of change of y is proportional to y. Solve the resulting differential equation…

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Q: Find the integrating factor of the non-exact differential equation: dy= (e2x+y-1) dx

A: Given differential equation is dy=e2x+y-1dx which can also be written as e2x+y-1dx-dy=0 Comparing…

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: determine the differential equation of the family of lines passing through the origin. x dy - y…

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

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Q: Show that y = cos xsin x is the solution of the differential equation y'+y tan x cos x

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Q: Consider the nonhomogeneous differential equation 1 y" (x) + y(x) = e # +: sin a

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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: dg dx =g (4-8)4=x* 2.

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Q: Let the function y = y(x) satisfy the equation (y − x)^2= 1 + 3(y + x)^2 Show by implicit…

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Q: Write an equivalent first-order differential equationand initial condition for y

A: Given Data The equation is y=2-ꭍx0 (1+y(t)) sin t dt.   Differentiate the equation y=2-ꭍx0 (1+y(t))…

Q: Find a particular solution of the differential equation COS X dy dx 1 +ytanx = cos x e cos x for…

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Q: What is the particular solution to the differential equation dx 1 + y = 2e-* with y = 1, dy -1 when…

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Q: Find a linear operating point model of the differential equation: d²x dx + 3 + 2x = sin x dt2 dt a)…

A: Consider the provided question, Given D.E, d2xdt2+3dxdt+2x=sinx We need to find a linear operating…

Q: Construct an autonomous first-order differential equation dy/dx = f(y) whose phase portrait is…

A: Consider the given figure. From the figure, it can be noted that the critical points are 0 and 2.…

Q: Find a function F(x,y) whose level curves are solutions to the differential equation (x2 + 4xy)dx +…

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Q: What is the linear differential equation of dy/dx+2xy+xy^4=0 using dv/dx?

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Q: Find the general solution of the first-order linear differential equation (y − 1) sin x dx − dy = 0…

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Q: Suppose that a certain population has a growth rate that varies with time and that this population…

A: First rearrange terms in the given ordinary differential equation  dyy=0.5+sint5dt since it is…

Q: Solve using the non-exact linear differential equation  [ytan(x)(cos(2x))-1]dx+csc(2x)dy=0 when…

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Q: What could be an integrating factor in solving the differential equation dx (tan y) x = sin y ? dy…

A: Integrating factor of differential equation

Q: Find the linear differential equation of the bernoulli’s equation dy/dx-y[1/(2x)]-y^5=0 using dv/dx.

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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: y' - y = sinx with an initial value of y(0) = 1. Solve the above linear differential equation using…

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Q: dy (sec x) dx eуtsin x

A: Given : The differential equation sec xdydx = ey + sin x

Q: At any particular time, the rate of change at which the vertical position of an object moving in…

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Q: Solve for the DE: (y²-1)dx + (2xy- Siny) dy =0 When x= -1 ; y= 0

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Q: a differential equation is classified as a homogeneous DE if one can directly isolate all functions…

A: A differential equation is classified as a homogeneous DE if one can directly isolate all functions…

Q: The Bernoulli's form of the differential equation xdy - [y + xy³ (1 + ln x)]dx = 0 is

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Q: If the differential equation corresponding to the family of curves y = (a + bx) e3x is given by dy =…

A: The given differential equation is d2ydx2=adydx+by....(1) Now, y=a+bxe3x is a solution to the…

Q: FIND THE GIVEN DIFFERENTIAL EQUATION Non Exact Eguation (xy + 1) dx tx (* + 4y - 2) dy - 0

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Q: (1+ex/y)dx + ex/y(1-x/y)dy = 0, a exact differential equation? If yes then, find the value of y.

A: Given differential equation is  1+exydx+exy1-xydy=0 Which is in the form of Mdx+Ndy=0. where…

Q: dx = x- y + 1 dt dy = y - x + 2 dt

A: Given: dxdt=x-y+1                       1dydt=y-x+2                       2 The above system of…

Q: Solve the first order differential equation. dy - y ln(y ecos x) dx = y sin xdx

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Q: The integrating factor of the non-exact differential equation (x°y? + y') dx – (y° + x*y)dy = 0 is

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Q: Obtain the differential equation of the family of straight lines with slope and y-intercept equal.…

A: We obtain the differential equation of the family of straight lines with slope and y-intercept…

Q: What is the general solution to the differential equation sin y (x + sin y)dx + 2x² cos y dy = 0 ?

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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: +2) dx + (y? Inx) dy = 0, is exact differential equation. Select one: True False

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Q: dy +2xy = e-* is The integrating factor of the differential equation

A: By using linear differential equations integrating factory  we can calculate..

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: The solution of the differential equation using dy = 5/1- y? dx variable separable is cOs 5х + с O…

A: Solve by variable separable

Q: Find the general solution of the first-order linear differential equation (y + 1) cos x dx − dy = 0…

A: We have to find general solution of the first-order linear differential equation: y+1 cos x dx-dy=0…

Q: If tan x sin x is an integrating factor of the differential equation + Py = Q then P =? dx

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Q: =x+x* +1 satisfies the differential equation (x +1): dy Show that y dx

A: Given the given differential equation is x2+1d2ydx2+xdydx-m2y=0 and the given value is y=x+x2+1m.

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.