We will introduce another method, variation of parameters method, of solving the following equation: y + p(t)y = g(t) (1) Step 1: Find a solution y1 of y' + p(t)y = 0 : yı = Step 2: Set y(t) = Y1w(t): Step 3: Substitute y(t) into (1) to get w'(t) = y'9(t) Step 4: Integrate: w(t) = f w'(t)dt = Syi'g(t) dt

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A: y''+y'-2y=0 Auxiliary eqaution m2+m-2=0

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

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Q: 2. Use separation of variables to solve (a) y' = -2y, y(0) = 1 (b) 4y' = y², y(0) = 4 %3D (c) y' + y…

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Q: Q2) Solve: y" - 5y' +6y=H(t-1), y(0) = 0, y'(0) = 1.

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Q: 9. (1) Find a second solution of the given equation. t²y" +2ty' - 2y = 0, t > 0, y₁(t) = t. (2) Find…

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Q: Find the solution of y" – by' + 9y = 16 et with y(0) = 2 and y' (0) = 1.

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Q: 2. Differentiate the following equations. a. Differentiate. 11 y 1=22²2²² 7x²

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A: General solution for the Homogeneous differential equations with constant coefficients

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Q: Find the solution. y' = y - xy³ e-2x A e2=x²(y²+c) B e2Y =x²(y²+c) (c) edx =y²(x²+c) (D D e=y²(x²+c)

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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.