Find the solution of the given initial value problem: y" + y' = sec(t), y(0) = 6, y′(0) = 7, y″(0) = −3. y(t) = 3+3 cos(t) + 7 sin(t) + ln(sec(t) + tan(t)) — t cos(t) + sin(t) In(sec(t)) X

Q: 6. Solve y sin (x) cos (x) with initial condition y'(7) = 1 and y(7) = 0.

A: y = 1/4 [ x - 1/2 sin2x] +x -π/4

Q: Solve the IVP y" + y' + 1.25y = 0 with y(0) = 3, y/ (0) = 1 O e-t/2(3cos(t) + sin(t)) O e (3cos(t) +…

A:

Q: Determine the order of the following differential equations: xy = 1 y" +x*y' = 2 (b) (y)3 +x 1 (d)…

A: The order of a differential equation is the highest derivative present in it.

Q: Find the solution r(t) of the differential equation with the given initial condition: r' (t) = (sin…

A:

Q: dy Solve the initial value problem: 4( sin(t)- + cos(t)y dt = cos(t) sin (t), 0 < t < T, y(T/2) =…

A: Here the first order differential equation is given as: 4sinty' +costy=cost⋅sin7t0&lt;t&lt;π,…

Q: Consider the following. x' = 4x + y y' = −2x + 2y,   X(0) = (−1, 2) The general solution is (x(t),…

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Q: (g) The solution of y' + (2/t)y (cos t)/t², y(7) = 0, t > 0, is Y COS (sin t)/t².

A:

Q: 3. Solve y' + cos(r)y = 2 cos z subject to the initial condition that y() = 2.

A:

Q: ) Using Huen's method to estimate the solution of the ODE y' = cos (xy?) ,y(1) = 2, h = 0.1 If y1=…

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Q: x" + 4x = S(t) + S(t-π) x(0)=0, x'(0)=0

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Q: Use the general solution y(t) = C₁ cos(t) + C₂ sin(t) + 6 to solve the initial value problem: y" = 6…

A: Step 1: Step 2: Step 3:

Q: Solve the equation y" +4y= S(t-4π), y(0) = 1/2, y'(0)=0 a. )= = cos(2t) + sin(2(t − 4π)µ(t − 4π)

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Q: Find the solution to the given equations: (a) y" + y' – 2y = cos(x) – 3 sin(2x), y(0) = 1, y'(0) = 2…

A: