1. Find dy given the following. Do not simplify your answers. da Va cos x etan(=ª) + log;(e – x) (a) y =

Q: 4. Find the general solution of the differential equation dy + y cot r = 1, dr COs z recalling that…

A: We can find the answer as below

Q: ve the following differential equations of dy r'y-r'. d = y* · cos(x). dx

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Q: y)dx + ( 2+ x + ye" )dy =0

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Q: (х+2)* x² – 4 dy 2y dx x? - 4 х —

A: Given  :        dydx+2yx2-4 = x+22x2-4

Q: H.W. solve the following D.E. 1. (x + √y² + 1) dx - (y-7) dy = 0 2. (ex + Iny+) dx + ( + Inx + siny)…

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Q: and Suppose z is a function of a and y, and tan Vy2 + x² = z*e6y. Solve for dx dy

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Q: Solve four questions of the following DEs 1- xy dy + (x² + y² ) dx = 0 dx 2- 2- y = e*/2 dy 3- (х +…

A: Explanation of the solution is given below...

Q: ... Q2: Solve the following differential equations: {[1+ y*] sin(xy) + xycos(xy)}dx + {[1+x*]…

A: Given problem is :

Q: Find a solution to the following equation in terms of Bessel functions. /" + 2n²ry = 0 y(x) =

A: Given that y''+2n2xy=0 Rewrite the equation, y''+2n2xy=0 Now substitute y=xu where u is a function…

Q: 6. Solve the following differential equations. xe²-In y? dx dy b) a) dy +y cot x = x dx

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Q: . mydx + nxdy = 0 xcos²y dx + tan y dy = 0

A: Let's find.

Q: (a) Find the general solution to the differential equation dy + (cot x) · y = 1. dx

A: dydx+(cotx)y=1this is linear first order differential its integrating factor is e∫cotx dx…

Q: Find a solution to the following equation in terms of Bessel functions. y" + 2n²ry = 0 y(x) =

A: Given: The given equation is y''+2n2xy=0 → equation(1)

Q: e the following differential equations: cos x dy +y = tan x. %3D dx

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Q: Solve the following Bernoulli's differential equation. y'+tany = e ,7x = e^.secy.

A: We have to find the general solution of given differential equation.

Q: 2. Solve the differential equation dy e?y-cot x dx tan?

A: Solve the above differential equations

Q: dy Solve the non-Linear differential equation cos - sin y(1 – O sin y).given that y(0) = 5. de

A: Consider the Bernoulli equation:y'+p(x)y=q(x)ynSubstituting v=y1-n in the equation changes it to…

Q: A. Find dy/dx of the following. 1. y = e" + eVinx + 2 In(ex) 2. y = er" 3. eln 4x + eln 4y = e + e"

A:

Q: 1. Use the substitution z = following differential equation xy, where z is a function of x, to solve…

A: Properties of integration  ∫1a2+x2dx=1atan-1xa+C∫xndx=xn+1n+1+CddxUV=UdVdx+VdUdx

Q: 3. Determine the Particular solution of this equation In terms ofY (xy2)dx + e*dy 0, as x → 0, y ==

A:

Q: dy x In (y) d.x x +1\2

A: To Solve the following differential equation:

Q: ( 3x?y + ev )dx + ( x³ + xe' – 2y)dy=0

A:

Q: Solve the following differential equation : d?y + 2 cos x· 2 sin x dx2 dy +2 sin x dx dy + 2y cos x…

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Q: -cosh(x)dx 18) St?cos(2t)dt S 2y²e»*dy 19) Sxeax+1dx dx Sx²e2*dx 20) S x-x2 ) (2?/ª x)°e-In(x²)e3×dx…

A: We have to find the integration.

Q: Solve the following first order differential equations: y' cos x + y sin x = 1, y(0) = 1. %3D y' = y…

A:

Q: (a) Find the differential dy. y = cos(x)

A: Differentiate the given function with respect to 'x' and find 'dy'.

Q: :Solve the following differential equation by Laplace: dy +24+ 5y = e-t sint dx dx ,y(0) = 0,(0) = 1…

A:

Q: Q2: Solve the following differential equations: {[1+ y*] sin(xy) + xycos(xy)}dx + {[1+x*] cos(xy) –…

A: Given            1+y2sin(xy)+xycos(xy)dx+1+x2cos(xy)-xysin(xy)dy=0

Q: Find the solution of the following Differential Equn 3) y'+2y = cos(x) 4) y' = (y-1) cot(x)

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Q: T. Selue the ff. differential epnotion ) xy (xdy tydy) = ky'dy; when yol; x=2

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Q: (4x'y – 15x? – y )dx +(x* +3y² – x)dy=0

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Q: 8. If y = xi, then the value of the differential dy as x changes from 16 to is (A) * (B) 5 (c) (D)…

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Q: Solve the following differential equation. (1+ sin y)dr = [2y cos y – r(sec y + tan y)]dy %3D

A: Consider the differential equation 1+sinydx=2ycosy-xsecy+tanydy and simplify it using the identities…

Q: 2. The exact differential d xdy - ydx what is the d(xe")= x?

A: Let's find.

Q: Solve the following differential equation: (sen(y) — ysen(x)) dx + (cos(x) + хcos(у) — у) dy %3D 0

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Q: (zy + x)dy + ydx = 0 %3D

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Q: What is the solution to the following differential equation? y = (x + y)², y (0) = 0 du As a hint,…

A: The given differential equation is  y'= (x+y)2, y(0)= 0  We have to find the solution of this…

Q: Solve the following differential equation.  dy/dx = tan y cot x — sec y cosx

A: To: Solve the differential equation dydx=tany cotx-secy cosx

Q: Q16: Is the differential equation (cos x+ In y) dx + dy 0 exact? %3D

A: Let us consider the given equation Mdx+Ndy=0 The equation is said to be exact if ∂M∂y=∂N∂x The…

Q: Q1/ Solve the following differential equation (x sin y)dy - cos y dx = x?dy %3D

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Q: 6) g(z)= . cos(t) dt

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Q: solve the following implicit ordinary differential equations. Зx*у + e% sect (ху) y' = - y , у (0) —…

A:

Q: 1) Find the solution of the following equation: y"+ ly 0, with y (0) = 3 and'y (0) = 3 with A<0. Is…

A: Let λ=-a2&lt;0 Then, y"+λy=0 ⇒y"-a2y=0 Auxiliary equation is m2-a2=0 ⇒m=±a So, the general solution…

Q: solve the following differential eqaution : (2x+y)dx-(4x+2y-1)dy=0

A: Solved below.

Q: (2) Find the differential of each of the following functions. In other words, for each of the…

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Q: 2. Find the following derivatives. (a) y = log; (xe*Y loz Leet (c) y = 38z2-5 (e) h(v) = e-2"…

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Q: 1 (In(11) xy e*y² dxdy

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Q: (1+x*)dy + x(1+ 4y²)dx =0

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Q: 14. e see" y dy = dx +x dy.

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Q: AA 1. Find dy/dx by means of differentials if xy + sin y = In x.

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…