dy + p(x) y = q(x) y" . If we substitution y = u' Given any Bernoulli DE the Bernoulli DE becomes a %3D dx Linear DE in x Homogeneous DE O. None of These Separable DE in x and y Linear DE in y

Q: + ( Xyz

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Q: If sin (x – y) = x³ then dy 1s dx а) dx dy _ ycos(x – y) – 3x² хcos(х — у) dy_ cos(x – y) – 3x? b)…

A: Solution is given by using sum and difference identities of trigonometry as follows :

Q: The solution of the DE: xy' - 4y = x°e* is O None of these y = x*e*(x - 1) + cx y = x°e* + cx* y =…

A: Topic- differential equation

Q: 2. Find if y=x² + 3x-7 and x=2t+1. d²y dt2 3. Find dx and d²y dx2 if x = t - and y= 1+t 1² 1+t

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Q: dy dt2 dt d'y 8x = 0 - dt?

A: Given that, d2xdt2+dydt=0d2ydt2-8x=0 Now take the derivative for the first equation with respect to…

Q: Find dy/dx for the following xVx² In y = In + 1 2 (x + 1) 3

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Q: Determine the linearity and solve for the general solution to the given DE * dx ecos y – x cot y dy

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Q: There exists a solution, F(x,y)=Dc, to (2- 2aye) da – (2ye + 3 sin y) dy = 0 such that - OF 2ye 3…

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Q: dy A. Find dx 1. y = In V3x²- 9x + 1 2. y = logs(x² + x- 1) 3. y= 2n secx 4. y =xln tanx 5. y = In…

A: 1. y=ln3x2-9x+132. y=log5(x2+x-1)3. y=2lnsecx       NOTE: As per our answering guidelines, we can…

Q: if x² + y² =t -- and x* + y* = t dy prove dx 1

A: Given, if  x2+y2=t-1t and  x4+y4=t2+1t2 To prove that  dydx=1x3y

Q: 1. Find x'e *dx if it exists.

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Q: X. 2. dx + cos y ) dy = 0 y A. xy - ysiny + cosy = C B. xy – ysiny - cosy = C C. xy + ysiny + cosy =…

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Q: 4. Find at the point (1,1,1) if ln(xyz) = 1 əx

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Q: dy Given y = u? - 1 and x = u2 + 1, find dx

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Q: -2x + 3x -x) dr- (sin y + y e (y e + +3y e) dy 0. x(0) 1 D 2r-- O 2y - y+ xr e O x+ 2x-y e-3y e+3e–…

A: The given differential equation is,(y2e-2x+3x2-x)dx-(siny+ye-2x+3yey)dy=0, x(0)=1

Q: Let y(x) be the solution for the DE. y' + y tan (x) + sin(x) JT If y(0) = In 2, then at x = 4 the…

A: Proceed as shown below

Q: Examine the change of the function and draw its graph: 2x-1 y =

A: Given: The function in x is given,           y=2x-1x3ex-1x Objective is to find the change of…

Q: 2. Compute Ja F · ds for F c(t) = (t , In(1+ t²), e*) for 0 <t < 1 VV, where V(r, y, z) = 4x² In(1+…

A: Find your answer below

Q: 1. dy dx \y+1 x2+1/ 2. " S"(sinx + cos2y) dx dy 3. S V(2x + y)" dx dy 1 3

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

Q: In (x + y + 1) dx dy ード

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Q: a When reduced to a linear DE of order one in z, the Bernoulli's equation dx becomes dz A + z( − 1)…

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Q: Which of the following DEs are first order linear DEs?

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Q: Given f(x, y) = 8x²y then the total differential df ,2, O 8xy dx + 8x² dy O 16xy dx + 8x² dy O 16x…

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Q: Let w = (sin(x) +7cos(y)) dy ^ dz + (z³ – y cos(x)) dz A dæ + 14xyz d A dy. Find dw. dw = dx A dy A…

A:

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.