For the following system æ' = Aæ, (a) find the general solution and express it in terms of the eigenvalues and eigenvectors of the matrix A. Determine the nature of the critical point (0,0) (i.e., stable/unstable, saddle, node, spiral, center, etc.). Sketch a few of the solution curves. -3 -2 2 -3

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A: a. Let S(t) denote the loan amount after t years. The equation governing S(t) is:dSdt=0.04S-kwith…

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A: To solve the given differential equation.

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A:

Q: 10. solve the following differential equation. dy +y= e*y 8 dx

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A:

Q: Match the differential equation with the appropriate integral curves, if it shown.

A: (a) The given differential equation is y'=-y2-y. Solve the equation y'=0 and identify the…

Q: Explain what method can we use instead of a Newton method when we don't want to find a derivative?

A: To find: Method can be used instead of newton method when we do not want to find a derivative.

Q: 2) Solve the equation y' = Y 4x²y + x

A:

Q: Write the capital letter E if the differential equation is exact and if NOT exact solve for the…

A: Given: 2x3y2+4x2y+2xy2+xy4+2ydx+2y3+x2y+xdy=0 To check: Given differential equation is exact. If not…

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A:

Q: The rate of change of a population of bacteria in a petri-dish can be described as the difference…

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Q: Evaluate the Differential Equation by Integrating factor. Solve: xy' = 3y + x^4_y(1)=7 Find the…

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Q: Solve the following differential equation. y"+y' - 2y = 0

A: Given:The given differential equation is .To Find:We have to solve the given differential equation.

Q: Find the differential equation of family of lines whose angle of inclination is 60 degrees.

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Q: Give 1 problem application of differential

A: We have to explain a real life example of differential equation.

Q: is there any application of second order or higher ordinary differential equation? can you you give…

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Q: dy = 3 sin (6x - 2y) dx

A: This is a problem of the differential equations.

Q: Give 5 sample problems for Exact Equations (Differential Equation). Provide step by step solution…

A: Let us give five sample problems of Exact differential equations and its solution in the next steps.

Q: A rumor spreads around a city, which has a population of 108,000. The rate of change of the number…

A: Let y denotes the fraction of population who heard the rumorThen 108,000 -y people not heard the…

Q: Please provide explanation every step in solution. Provide simple explanation in the right of every…

A: Problem 1 :- x + xy =C;   C is arbitrary constant. x + xy =C…

Q: Consider a differential equaUion -x2 y' = xy + xe

A: we have been given a differential equation with initial condition y(0)=0 y'=xy+xe-x2

Q: Is there perhaps an easier way to approach these questions? Im quite new to differential equation.

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Q: Find appropiate in tegrating and solve the equation an 3 323? dx + こ

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Q: Solve the following differential equation using variation of parameters. y" + y = sin(x)

A: Given differential equation is    The auxiliary equation of above differential equation is…

Q: oM Differential Equation Show a complete solution ySy 13yty =0

A: Consider the given homogeneous 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.