Solve the following first order differential equations: Og²-cos (0) sin (0). g(1–02) dg i. g(0) = 2. de dv ii. = mg – bv2 dt such that m is mass, g is gravity, b is constant, subject to v(0) = 0.

Q: sec2 a tan ydx+ sec? y tan rdy = 0.

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Q: (1+sinx csx) 6- dx dy= e sinhy Cos 2X

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Q: Consider the DE: − (8x³y – 32)dy = (12x²y² – 20)dx. - - A) Show that the differential equation is…

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Q: Determine the solution of the differential equation dy y cot x = cosx dæ

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Q: 2yy" = 1 + (y')² 2

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Q: 1.) 2y(4х — у) dх + (2x? — Зху — у3) dy %3D0

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Q: (x Sin -y cos + X cos dy

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Q: dI + 501 = 5; where I(0) = 0. dt

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Q: Suppose that you have $11,000 in a rather risky investment recommended by your financial advisor.…

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Q: For what value of is the differential equation (6zy + cos y) dr + (3ka²y? – 3y?) dy = 0 exact?

A: Exact differential equation

Q: a) Solve the following first-order differential equations: ER -y- = 2x, given that when y=0, x=+2

A: The given differential equation is:

Q: Solve the following differential equations, giving y in terms of x. dy (iii) cotx + 2y = sin 2x. dx

A: Let us consider a differential equation of the form dydx+Py=Q where P and Q are function of x  To…

Q: dy -y- dx 2x, given that when y=0, x=+2

A: We need to solve the given differential equation with its initial conditions. As the equation is of…

Q: Determine the order and degree of the given differential equation: 1 dy -ky dr 100 dx

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Q: (B) Solve the following differential equation: 3y cos 3x dx - sin3x dy = 0

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Q: Solve the given differential equation : dy x² – 2xy = 3y*, y(1)=1/2 dx

A: We will find out the required solution.

Q: Solve the following first order linear differential equations.   y' + y cosx = sinx cosx

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Q: а. (у — cos?x)dxх + сosxdy %3D 0 b. ydx %3D (еУ + 2ху — 2х)dy

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Q: Solve the following differential equation cos>x Y = xV dy = xV1-y dx Select one: O a. y= cos(xtanx +…

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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.