Which of the following is the solution of the initial value problem (2) + 2 / v(t)dt = -2y(x), y(0) = 1 ? 0. y(r) = (cos r – sin x)e¬ O y(x) = cos x + sin x O y(r) = e- + e* O y(r) = e" (coS r + sin r) O y(x) = 2e¬ – cos I %3D -

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A:

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A: Find the general solution of (a) Using undetermined coefficients.(b) Using variation of parameters.

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A: The given equation is; (ex + 2xy2) dx + (2cos2y + 2x2y)

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A: Using Derivatives.

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Q: The special solution to the equation * (D²-3D+4)y(x)= 4sin(2x) Y,(x) = Excos(2x) у, (х) cos(2x) -…

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Q: Solve

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Q: 2. Find all solutions: dt dy dx = 4x + y x + 4y' x > 0.

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A: To find -

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A: Solution of the given question is like as

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Q: Find the general solution dy + cos(x)y = cos(x) dx O y = 1+ ke-2 sin(x) O y² = 2 sin(x) + c y =…

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A:

Q: 22) Use Euler method to estimate the solution of the ODE y' (xy?) ,y(1) = 2, h = 0.1 at x = 1.2

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Q: Find the general solution of y" + 12ly = 0. Oy(t)=c₁e-12¹+c₂e Oy(t)=c₁e¹¹+c₂e Oy(t) = c cos 11t+c…

A: This question is about ordinary differential 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.