2. (a) Prove that the linear differential equation dy + P(x)y = f (x) - dx has an I.F. eſ p(x)dx (b) Find the solution of the nonlinear linear IVP dy 2x + 1 -y = e¯2xy2 dx

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A: We have to find explicit solution of First order linear differential equation:

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Q: 2. Determine the equation of the following function. State your answer as a piecewise function. y 10…

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Q: (x² + b²)dy = 2x[(x² + b?)² + 3y]dx; y(b) = 4b*;

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Q: Let f(x) = x² + f(t)dt. (1) Find f(0) and a first order linear differential equation that f(x)…

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Q: Find the general solution of the first order differential equation 2xy(dy/dx)=x2-y2

A: The given differential equation is a homogeneous. See attached file for a step by step explanation.

Q: Solve for a linear equation? P(t)y'' + Q(t)y' + R(t)y = S(t)

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Q: © (y?(x+1) +y) dx (2xyer) dy=o 2, diferansigel denklemd'i

A: Given differential equation is y2x+1+ydx+2xy+1dy=0

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Q: Match the differential equation dy / dx = sin 2x with its slope field.

A: Match the differential equation dy / dx = sin 2x with its slope field.

Q: Q1) Find the exact sol of differential equation xy'+ y 2x, y(1) = 2

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Q: ) Solve the equation (IVP) (1 +x²) – x(1+ 2y)y' = 0 y(1) = 0 %3D

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Q: Def (Function): A binary relation RCX X Y is called a function from X to Y, written f:X →Y if -…

A: The concepts have been explained with examples.

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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.