dy 2y sin 3t equation dt (a) Solve the differential by using Linear differential equation method. [2.5 Marks] (b) Check whether the given differential equation is exact or not. (2x y+4x-12xy +3y - xe' +e*) dy+(12x*y+ 2.xy +4x -4y' +2ye -e' )dx=0 If yes, then find the exact solution of the differential equation. [2.5 Marks]

Q: 2. 2xy dx + (x² + y²) dy = 0.

A: The given differential equation is 2xy dx+(x2+y2) dy=0. The solution is obtained by: The exact…

Q: O Solve the differential equation y' + y cot x = y* sin x.

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Q: (e"siny + tany)dx + (e*cosy + xsec*y)dy = 0

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Q: (бх + у?)dx + у(2х — Зу)dy %3D 0

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Q: dx - x = (-²/cost) x³ dt 2t 2

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Q: Given, G+) dæ + (41) dy = 0 is an exact differential equation. Determine the value of A.

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Q: (D3-D²)y =0

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Q: Tom wants to invest $500. He invests in a company that predicts his investment will double in value…

A: Initial investment is $500 and the money gets doubled in 3 years.

Q: Differential Equation Q:(x² - 21y)dy = (x² – 2xy )dx.

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Q: Solve the differential equation y' = x + y by making the change of variable u = x + y.

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Q: (3x²y+2e²y+3)dx + (x³ +4xe²y-sech² y+2lny)dy-0

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Q: (cos y+ y.cosx-ec*.sin x)dx+(sin x – xsin y)dy =0 cos.x

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Q: product rule to 3. Use the substitution uy to solve the differential equation xy' + 5y = 3ay

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Q: Solve for the function y that satisfies ty' = 2y + 4t³ cos(4t) = 0 {

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Q: d'x d²x dx + 7x = 3 sin 8t. dt 5. +2. dr3 dt2

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Q: Find the general solution: y" – 8y' = 10x + 3

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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.