Find all the critical points (equilibrium solutions) of dx dy = y+ 5xy. dt dt

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Q: Find the general solution of the differential equation: dy/dt=−y/t +7 Y(t) = ?

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Q: Is the differential equation linear? dy dt + y2 = x

A: The given differential equation,     dydt+y2=x

Q: Find the particular solution of the differential equation that satisfies the initial condition(s).

A: Given: f'(x)=6x f(0)=8 Integrate the equation. ∫f'(x)=∫6xf(x)=6x22+Cf(x)=3x2+C

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Q: Find the particular solution of the differential equation that satisfies the initial condition. dy…

A: Given differential dydx=116-x2 dy=116-x2dx Integrating both sides ∫dy=∫116-x2dx We know that…

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Q: Find the solution to the initial value problems using integration. dH/dx=3x, H(0)=1…

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Q: For the autonomous first-order differential equation, y' = y2 – 3y – 4 find the critical points and…

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Q: . Find the integrating factor of the first ordered linear differential equation, (x + 3y)dx – xdy =…

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Q: dx -x+3у dt dy -3х + 5у dt

A: Given the differential equation is  dxdt=-x+3y......idydt=-3x+5y..........ii…

Q: Find the particular solution of the differential equation dy/dx+ycos(x)=4cos(x) satisfying the…

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Q: Find the solution of the differential equation dy/dx=x/y that satisfies the initial condition…

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Q: Find the solution to the differential equation dz = 2te?z dt at passes through the origin.

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Q: dy 1. + ty? = 0 dt

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Determine the general solution to the differential equation dy +4x° = yx dx Use a "c" to denote the…

A: We have to find the general solution of the differential equation dydx+4x5=yx5.

Q: Find the function y(t)y(t) that satisfies the differential equation dy/dt−2ty=−3t^(2)*(e^(t^2))…

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Q: Find the integrating factor of the differential equation dy + 2xy = x³ dz %3D a. b. c. 2 In (r) d.

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Q: dy dy -4 =0 dx dx O 2 and 6 O 2 and 4 O 1 and 6 O 1 and 4

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Q: Solve the given differential equation with boundary condition. y' – e V = 0, y(1) = 1.

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Q: Find the equation which satisfies the separable differential equation dy – 18x dx with the initial…

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Q: dy y X + 2 dx 3. || 3.

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Q: Find the unique solution to the differential equation that satisfies the stated condition. dy 2x +…

A: We have to solve the following differential equation

Q: Find an implicit solution to the initial value proble dy = y? – 2y, dx y(1) = 3. -

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Q: Use separation of variables to find the solution to the differential dy y²(4 + t), if y = 2 when t =…

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Q: Find the general solution of the differential equation: dy + 7. t dt Use lower case c for constant…

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Q: Categorize the Differential Equation. (x – y)dx + (3x + y)dy = 0

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Q: Find the particular solution for the differential equation dy/dx= k(M-y), y(0)=0; k,M-constants

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Q: Find the function y(t) that satisfies the differential equation dy dt and the condition y(0) = 2.…

A: Let us consider the given function dydt+P(x)y=Q(x). To solve the equation using integrating factor…

Q: What is the solution of given initial value problem? d²x = y + sin t dt2 d²y dx + cost dt dt2 æ(0) =…

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Q: 1.Find the critical points, classify each critical point as stable, unstable or semi-stable . dy 10…

A: Given: dydx=10+3y-y2 To Find: a. Critical Pointsb. Classify each critical point as stable, unstable…

Q: With the aid of an appropriate integrating factor, calculate the initial value of the equation…

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Q: dy x sin x y(0) = –1 6. dx y

A: Given : dydx=xsinxy. By simplifying, we get: ydy=xsinx Take integration on both sides, we get:…

Q: Show that: (xy? ) is an integrating factor of the differential equation dx dy хуз у4 r.IV 2y dx + 3x…

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Q: Solve the Bernoulli equation for y. dy 2y + y*. dt Use the following initial condition: y(0) = 1.

A: We need to solve the Bernoulli equation for y. To solve given differential equation first using…

Q: Find the equation which satisfies the separable differential equation dy – 14x dx with the initial…

A: We will find out the required solution for given differential equation.

Q: Find the function y(t)y(t) that satisfies the differential equation dy/dt−2ty=−3t^(2)*(e^(t^2))

A: Consider the provided question, We have to find the solution of the given D.E,

Q: dy = xe', y(0) = 0 dx %3D

A: dydx=xey⇒dyey=x dx⇒e-y dy=x dx⇒∫e-y dy=∫x dx⇒-e-y=x22+C⇒e-y=-x22-C⇒-y=ln -x22-C⇒y=-ln -x22-C

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

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Q: Find the general solution of the given higher-order differential equatio y(4) + у" + y" %3D 0 y(x)…

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Q: Find the differential equation of dy/dx = x(1+y²)/4y.

A: To solve the differential equation dy/dx=x(1+y^2)/4y

Q: Find the function y(t) that satisfies the differential equation dy 2ty = 6te" !! dt and the…

A: To find the solution for the given differential equation

Q: Find the particular solution of the differential equation dy xy+y when x = 1; y = 1. %3D %3D dx xy+x

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Q: Find the solution of the differential equation dy dx = 5 x cos?(y) which satisfies the initial…

A: Given: dydx=5xcos2y For finding solution of given differential equation, we will use variable…

Q: y' tan x = a + y, y(T/3) = a, 0<x< T /2

A: If a differential equation is given, then isolate the similar type of variable on one side. Then…

Q: dy Write down a differential equation of the form dt solutions all approach y as t→∞. y' = 78 = ay +…

A: It is given that y=78 as t→∞. The objective is to find the differential equations of the form…

Q: dy ト+e dx

A: Calculus