Use the method of characteristics to solve the first order equation Ug – 2uy = 3 with u(x, x) = sin(x).

Q: dy Q2) Solve x- 2y = x³ tan 2x dx

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Q: Use the 2 solutions Bernoulli's equation y' + -√√y=0 y x

A: The given differential equation y'+yx-y=0. We have to find the solution of the differential…

Q: The y' of the given function is (1–2 sin? 4x) y

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Q: 1. find the linear approximation tof (x) at x = xo. Use the linear approximation to estimate the…

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Q: 2) Find the derivatives of a) y = 7 - 6x-x² b) y - ³x 8 √x

A: Given :(a)y=7-6x-x2(b)y=-8x

Q: By Lagrange's formula, prove that y =y3-0-3(ys-y- 3) + 0-2 (y_ 3 -y_5).

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Q: The general solution of y' x2 can be written in the form

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Q: Solve y" – 4y' + 8y = e2" + sin 2x 3.

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Q: Find the general solution of the equation: y' -2y = 2 sin(3t).

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Q: Solve the DE (D-1)y= 3 sinx+ 22 - 2x°2

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Q: +3x2 b. Find (y)? = sin³(cos³(* *3*)) %3D dx 2

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Q: (D² – 3D+2)y= sin3x

A: We will find out the required general solution.

Q: f(x) = cos3(4x-1) Differentiate the equation

A: Given that: f(x)=cos3(4x-1)

Q: dy Solve sin -1 | = x +y dx,

A: Sin-1(dy/ dx) = x+y => dy/ dx = sin(x+y).

Q: y = x tan(x+C) eliminate the arbitrary constant

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Q: Solve the DE y' = y sin x.

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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.