What is the MOST acceptable method to determine the general solution for the function: y" – y'- 2y = 2x + tan2x

Q: 3. (4x³y5 sin 3x + 3x*y$ cos 3x) dx + 5x*y* sin 3x dy = 0 y(0) = 1

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Q: (1) x² + 3xy+y? = 4 (2) -=y² +1 x-y

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Q: Find the particular solution for: y' sin(2y) - cosx = 0, x =when y = 0 %3D 2

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Q: use appropriate substitution to solve differential equatio dy/dx-(2/x)y=-x^2y^3

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Q: Solve for the differential of y when y = sinæx, x=-, and dx=- 3 2 4 4 -iN

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Q: find a particular solution yp of the given equation. primes denote derivatives with respect to x.…

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Q: Find the particular solution for: y' sin(2y) – cosx = 0, x =when y = 0 %3D

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Q: 5. Find of the parameters: x = sin 2t and y = - cost at t = dx %3D

A: Topic = Derivative

Q: . (4x³y5 sin 3x + 3x*y5 cos 3x) dx + 5x*y* sin 3x dy = 0 y(0) = 1

A: See the solution.

Q: Solve using Substitution Method. y(x Tan x + In y)dx + Tan x dy 0

A: The substitution method as follows, y (x tanx + ln y) dx + tanx dy = 0

Q: Find the general solution to the ODE using the method of Variation of Parameters: y" + y= cos² x

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Q: 3. Find y' for y= cos(sin² x) 4. If x=y√/1-y², find y dx

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Q: What is the general solution to the differential equation (3 tan x – 2 cos y) sec?x dx + tan x sin y…

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Q: [y²e + √elnx dy-(xy) sin² ( * O) + (---) (-) sin² tan² ,dx ey+Inx dy y(In2x-lny) -ex. dx = 0

A: We can solve this using substitution method of ordinary differential equation

Q: Find the differential of the function y=√x3+4x at x=2.

A: Given the function:

Q: - sinx) dx 2. 1. (COSX (ax' +b)*x dx 2. 2/3

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Q: 5y + sin y = x²

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Q: Solve exact equation 2x -)dx + (2x cos(2xy) + 8e²")dy = 0 x² + 1 (2y cos(2ry) + with initial…

A: We will solve the problem.

Q: dy tan tan x = 0 dx coscos x +

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Q: Find the general solution of y'= sin²xcosy.

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Q: Find dy/dx for y = 3[(sin-(e-3x*))2

A: Given,          y=3sin-1e-3x22

Q: 2- X %3D +2 3- Coshx dy +(y sinh x+e) dxo 36

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Q: = sin(5x) for y(0) = 2

A: the solution is, y = (11 - cos5x)/5  The detailed solution is as follows below:

Q: 2 (b) - 2y dx +(2y tan'(x )-2x +sinh (y))dy = 0

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Q: Solve for Txyz given the function T(x, y, z) = z tan (In x - √y)

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Q: Find the particular solution for the given separable equation when y(0) = 3. 1 dy = ysin(2x) 1? dx

A: To find the particular solution for the given separable equation when y(0)=3

Q: Find y' by implicit differentiation. cos(x) + √y = 2

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Q: x + y sin 2 ) dx x sin 2 dy = 0 -

A: The solution is given in the next step.

Q: Apply variation of parameters to find a particular solution of y ''' - y' = tan x

A: The given differential equation is y''-y' = tan x.We have to solve this using the variation of…

Q: Find the differential of the function y=xxe2x at the point x=1.

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Q: Find the differential of the function y=2x2+3x+1 at the point x=1 when dx=0,1.

A: To find the differential of the given function at point x = 1 when (d x) = 0, 1.

Q: Find dy/dx by implicit differentiation. 2(x^2+y^2)^2 = 25(x^2-y^2)

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Q: 2. Find the length of the curve: y = 2 In (sin (÷x)); -< x

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Q: Use variation of parameters to find the particular solution to y"+y' – 20y = - 3400 sin(3t) Y(t) = |…

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Q: 4- cosh x2 dy + (sinh x)y = e-* dx

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Q: 4- Find dy/dx for y = 3[(sin-"(e-3x*)²

A: f(x) = 3arcsin2e-3x2f'(x) =ddx 3arcsin2e-3x2=ln(3)·…

Q: The antiderivative of the function sin (Gx+7) is:

A: Given : sin12x+7

Q: 8. Find dy/dx- y = sin (1 + x^2/1-x^2)

A: I have stated the used formulas in the solution

Q: tan(4x + 8). Find the differential dy when x = Let y 1 and dæx 0.3 Find the differential dy when x =…

A: In the given question we have to find dy of the function at both of the given value.

Q: Find2 of the parameters: x = sin 2t and y = - cost at t =

A: In this question, we need to find dydx. It is given that x = sin 2t and y = -cos t

Q: Find the differential of the function. y=x^4 (sin(8x))

A: topic:-  derivatives

Q: Solve (y sin x + xy cos x) dx + (x sin x + 1)dy = 0

A:

Q: Solve for the differential of y when y=sinxx: x=-, and dx 3 2 2 2 4

A: y=sinπx, x=13, dx=12

Q: 1I) (3y cos(3x)dx-sin(3x)dy)/ y 0

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Solve for the differential of y when y=sinzx, 1 x=-, and dx =-. 3 2

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Q: 2. Solve (sin y – 3x² + 5)dx + (y +x cos y)dy = 0. (Test for exactness and solve)

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Q: Determine the general solution of y" + y = tanx using variation of parameters

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Q: Use variation of parameters method to solve b. y" + y = tan x

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Q: Solve for the differential of y when y- sinax. x= and dx O o o

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Q: 2. Find the linear approximation to y = sinh (3x) at x=2. State your answer in both exact form and…

A: Find the linear approximation of f(x) at a point x=2

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.