Find all equilibrium points of X' = x(0.3 – 0.01y) y = y(15 – y+25x)

Q: What are the P(x) and Q(x) of y' =y-xy³e2Xrespectively?

A: Given the differential equation is: Since

Q: y = V In(5x + 7)

A: In this question, we use the chain rule to find the derivative of the function .

Q: ' (x² +2)+4x(y² +2y+1)=0, y(0) =1.

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Q: Find y': y=- Vx* + 4

A:

Q: If the equilibrium of dy/dx = y - sqrt(y) when y>0 is y=1, is it a stable or unstable equilibrium?

A: Given dydx=y−y, when y>0 We have to check whether y=1 is stable or unstable equilibrium. Note:-…

Q: let h(y)=(y-3y2)5(y2+2)6  h'(y) in simplified form.

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Q: Find y as a function of t if 16y" + 16y + 4y = 0, and y(1) = 2, y'(1) = 3. y =

A: The given differential equation  and the initial conditions .The objective is to find the solution…

Q: Find y'. y = V In(7x + 5) y' =

A: Given the function y=ln(7x+5)         ........(1)

Q: Find y as a function of tif y(t) T y" + 16y + 80y = 0, y(0) = 5, y'(0) = 2.

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Q: Find y as a function of a if y(1) = -4, y'(1) = -9. y x²y" + 2xy' - 6y = 0,

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Q: Find y as a function of a if y(0) = 6, y'(0) = 24, y"(0) = 108. y" + 36y' = 0,

A: y′′′+36y′=0y(0)=6,y′(0)=24,y′′(0)=108.The characteristic equation…

Q: Find a slope of the solution of y' = t – y at (3,1).

A: We have been given a linear differential equation dydt=t−y ______(i) (As y′=dydt)We have to find the…

Q: Find y as a function of t if y(0) = 2, y'(0) = 5. y(t) = 100y" +9y = 0,

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Q: Assume that  dx1/dt= x1(2-x1)-x1x2 dx2/dt= x1x2-x2 a) Graph the zero isoclines. b) Show that (1,…

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Q: Find y' and y'' given x2 +xy +y2 =1

A:

Q: Find y'. 2 O|N 9 y=x + 2x

A: Given value,     y=

Q: Find y as a function of a if y" − 3y" − y + 3y = 0, y(0) = −9, y'(0) = −8, y'(0) = 7. y(x) =

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Q: V3 (9) 1 x' x(0) = V3 - 1

A:

Q: 1. Find y'. (a) v5æy + 2y = y² + xy³

A: Differentiate wrt x

Q: Suppose that, p* is a market equilibrium price such that Qª = Q* = Q*. So the system of equations of…

A: Consider the provided question, We have to find the derivative dQ*dθ and dp*dθ. Since , at…

Q: Find a > 1 to express y = 3(2/9)x in the form y = 3(a−x)

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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.