tan(6 ex) is a solution of the differential equation y' + y = 3T with the initial condition y( - In 6) = Check whether the function y = e 2 1+ 36 e 2x Find y' for the function v=e -X tan -1 (6 e X)

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A: Given

Q: For the second-order differential equation y" + 9y = 6 cos x: a. Show that y = cos x is a solution.…

A: The given differential equation is: y''+9y=6 cos x

Q: The solution of the differential equation 5/1 – x2 ? dy dx 7/1 - y? = 0 is - 5 sin-x – 7 sin-y = C 5…

A: Question is solved.

Q: 6. Solve for the general solution of the differential equation using exact equation [2x + y cos…

A:

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A: Here I am attaching image so that you understand each and every step.

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A:

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Q: 3. Show that the differential equation (1 – 2y + x In a)dx + (e2v – 2x)dy = 0 is exact and find its…

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Q: Find the particular solution of the first-order linear differential equation        y′ + y = 6ex…

A: y'+y=6ex Comparing with y'+Py=Q, we get P=1 &amp; Q=6ex Now the integrating factor is, IF=e∫P dx=e∫1…

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A: Given , Differential equation is  y-xsinx+2cosxdx+x2cosxdy=0 Now ,we write the given equation of the…

Q: Consider the differential equation y" - 2y' + 17y = 0; ex cos(4x), eX sin(4x), (-∞, ∞). Verify that…

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Q: 2. Find the differential equation for x(t) when of [9x()* - x(O*]dt = 0 %3D Then, solve the…

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Q: Find the general solution of the first-order differential equation                    (2y − ex) dx +…

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Q: Consider the differential equation y" - 2y + 17y= 0; ex cos(4x), ex sin(4x), (-∞o, co). Verify that…

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Q: 6. Solve for the general solution of the differential equation using exact equation [2x + y cos…

A: Given differential equation is  [2x+ycos(xy)]dx+xcos(xy)dy=0

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A: Given that  The differential equation  To find the general solution

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A:

Q: The differential equation formed by eliminating arbitrary constants a ,b andc: y = ax + bx + cx + 8…

A: In this question, we have to find the differential equation by eliminating parameters.

Q: b) Euler's method is used to solve a first-order differential equation dy dx from x = 0 to x = 4

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Q: 2. Solve the differential equation using undetermined coefficients satisfying the given conditions.…

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Q: 3. Solve the Euler-Cauchy differential equation d²y dy 3x +4y= ln² x – In x dx² dx

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A:

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Q: 2. | Determine the general solution of the given differential equation y" -6y" = 3- cos x

A: The solution is given as