xp xp -3x Fxe+zメ %3D %3D xp 6+! hp xuis (P) dy = 2xy+3yZ Let y=Vx (8) dy- x²+y= 4. *Sec" xp (b) y tanx dy = (4+4*) Secx Fip M) xp Solve the following differntial equation

Q: SA de is equal to sec-1(/x) x-1 O 4 sec 3/2 O 2 [sec-1(/). 3x +C +C O 2 (sec-(V)]/2 + C

A:

Q: 3- y = sec x prove that d? y + y = 2y3 dx2

A: We have to prove the given differential equation to be true.

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A:

Q: 3u + 4v) dv 6. v(2up - 3) du + (3u²u 7. (cos 2y = 3x²y²) dx + (cos 2y – 2x sin 2y – 2x³y) dy = 0. +…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

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A:

Q: (3 Points) Solve the IVP. (1 + x² + y² + x²y² )dy = y²dx, y(-1) = 1 O + y = tan-x + 4 O = = cosx +…

A: The solution is, y - (1/y) = tan-1(x) + π/4 The detailed solution is as follows below :

Q: Use a change of variables or Table toevaluate the following indefinite integrals. Check your work…

A: Given:

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A: Rewrite y' = dy/dx and rearrange to get, 3xcosxdx = (2y + e3y)dy

Q: If cos(4x – y) = x+y, then dx A -1 - sin(4x – y) 2+4 sin(4x-y) (B) sin(4x-y) 1 1+sin(4x-y) C) 1+4…

A:

Q: y= (1+x?)tan x- x? y' = 1 + xtan1-2x y' = 1 + xtan -2x y' = 1 + 2xtan 1-2x y' 1 + 2xtan -2x y'…

A: In this question we are required to calculate the derivative of the function.

Q: Find the amplitude, the period, and the phase shift and sketch the graph of the equation.

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: 3. y" y'-y = cos(5t) - sin(5t); y(0) = 2 and y'=5

A: First find the commentary function then particular integral and then use the initial conditions as…

Q: 2) x – 2y = x°cos4x 3) x = y+x³ + 3x² – 4) +x = 4cos2y dy

A: 2)  xdydx -2y = x3cos(4x)⇒ dydx -2xy = x2cos(4x)This is a linear differential equationI.F. =…

Q: Qlif y= fcus and u=x46x +5 U =X and - 2u -1, Sind dy dx

A:

Q: 5) -6 = -sec 0 – sec² 0 – 4 %3D TT 5T A) { 3 2n 4T B) (0, 프, 3' 3 3.

A: The given equation is -6=-secθ-sec2θ-4. Simplify the given equation as follows.…

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A:

Q: 2z2 cos 5z dz EVALUATE.

A:

Q: #5 ở V - (2xy sinz) - (3y~); + (5x> y? z?)k .* and vx ů. ealeulate

A:

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A:

Q: Use a change of variables or Table toevaluate the following indefinite integrals. Check your work…

A: We have to evaluate ∫sec4w tan4w dw. From the table we have ∫secax tanax dx=1asecax +C Therefore,…

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A:

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A: Given: cosxsecx=2sinx

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A:

Q: find δƒ/δx and δƒ/δy. ƒ(x, y) = cos2 (3x - y2)

A: Consider the provided provided function, fx,y=cos23x-y2 Find the partial derivatives of the function…

Q: Exercise No. 2. Use Elimination of Constants by Isolation of Constants. Show your COMPLETE AND CLEAR…

A:

Q: 4) y'-4y = 2x-4x 6) y'+2y = cos(x) 8) y'=(y-1)cot(x)

A:

Q: -1 tan y2 y2 +1 n¬² y tan-1 y ) dy

A: We can integrate this integral by using the integration by substitution technique. Here we have to…

Q: 43. y= 2cotf x 2 44. Y=: G- Sec 2 45. y= 4 csc(2x + 7) 46. y= tan( x +

A: Consider the functions of the form y=AgBx-C+D where g is any basic trigonometric function. Then, the…

Q: 1. / 2dx 3D 0 + С %3D С 2. Sx²dx = 2x + C %3D 3. S 5x*dx = x5 1 4. Sdx = + С 2(х2-5) x2-5 5. ſ tan x…

A:

Q: 1. (D² 2. (D² -3D+2)y=sine* -3D-4)y=16x-50cos2x :

A:

Q: 1. [5an2f elan 28 sec² 2 Båß 3. e +1 2x e2x +2e* dx e* +1 4. |(30shm +ecoshm' 2.

A:

Q: ) y =-3 cos(3x) y 3+ X -2t -3+

A:

Q: æ' = y – 5 sin (3t); y/ = -4x + 17 cos (3t) , ift = n, x = 7; y = -4

A:

Q: y sec2(tan-ly²) dy 1+y+ tan ( tan-ly²) + C A) True B False

A: We have to find the value of the integration  ∫ysec2tan-1y2dy1+y4 we find the value of the…

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A:

Q: b) dr cos² #√5 + tanz c) ₁ dt (3-5t)²

A:

Q: . (3tanx-2 cosy)sec xdx+ tanxsin ydy = 0 %3D

A: To solve given differential equation first we check given differential equation is exact or not.Here…

Q: 1. y = xsin(x + A) 2. y = C,sin3x + C2cos3x + x² – 9 3. y = 3Asinx – 2Bcosx

A: Please see the below picture for detailed solution.

Q: 2U y'sy tan(x) 2) yy's 2Xes

A:

Q: Obtain the solution (3tan x-2cos y) sec^2x dx + tan x sin y dy = 0

A:

Q: The SPecial solution th the differntial equation. y+2y"+yドれ+y=leg y= Cas(2メ)+ sin(eメ】-2x 1 Y= -…

A: The given equation is; x4y"" +2x3y"' +x2y" -xy' +y = log(x).

Q: Solve osdinary DIPPedential Eguation + qy 6 Cos(3t) Y(0) = 0 %3D Y'(0) = 0

A: Consider y=emt be the solution of the homogeneous part. The auxiliary equation is m2+9=0. Solve the…

Q: Solve (cos?2x)dy3Ddx Sec2x(tan2x) O a. y= +C O b.y= Sec2x + C 2 %3D Oc.y=tanx+c tan2x O d. y=- + C 2

A: Rewrite the equation to separate the variables. 1sec22xdy=dxdy=sec22x dx

Q: Solve tan? x csc° ydx = dy. tan x = - cos y + [(cos³ y/3] + c O tan x - x = - cos y + [(cos³ y/3] +…

A: We will find out the required solution.

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.