Consider the autonomous differential equation  dx/dt=-7(x+1)(3-x)(x-5)^2  Find the equilibria, draw a phase line for the differential equation, and then classify the equilibria. Finally, sketch representative solutions to the differential equation based on the phase line.

Q: Use an appropriate substitution (4-5 a cos² to solve the differential equation (-) ) ª dx - x dy =…

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Q: Solve the differential equation (D+ + 5D² + 4) y = sin x + cos 2x.

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Q: y = C, cos 3x - C sin(-3x)

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Q: Determine the solution of the differential equation: (3tanx - 2cosy)sec²x dx + tan xsin y dy = 0

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Q: Solve the differential equation: dy + (2x – 7)y dx 8x9

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Q: Solve the exact differential equation: (2x+1+2xy) dx + (x2 +  4y3) dy = 0

A: (2x+1+2xy ) dx + (x2 + 4y3) dy = 0  on comparing with   Mdx + Ndy  , we get ,       M =…

Q: Find a differential equation whose general solution is y = c₁e²t + C₂e-2.

A: Note: Your general solution should be: .The differential equation for this general solution needs to…

Q: Solution to this differential equation: (y2-3y-x)dx + (2y-3)dy + 0

A: the given differential equation is the first order linear differential equation.we will solve this…

Q: Give an example of a differential equation.  Identify its type according to linearity, form, order.…

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Q: 5. A differential equation is if it can be written in the form f(y)d(y) = g(x)d(x)-

A: A differential equation is ORDINARY if it can be  Written in the form f(y)dy = g(x) dx .

Q: Solve the following linear system and sketch its phase portrait * = [¹ =1] x.

A: Here for a given homogeneous matrix linear system we have to solve it and then sketch the phase…

Q: Find the linear differential equation that is satisfied by y=xe-xsin3x+2e-xcos3x.

A: Let's find linear differential equation.

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.