Solve the initial value DE y - ytanz = sinx, y(o) = 1 5-Cos 2x 5-Cos 3x 5-Cos 2x Cos 2x A) y = B) y = C) y = D) y = Arnsx End of document

Q: Find formulas for the following general indefinite integrals to verify results (7), (8), and (10) in…

A: We’ll answer the 7th question since we answer only one question at a time. Please submit a new…

Q: Solve the initial value problem. * = et sin (et - 4), y(ln 4) = 0 %3D O A) y = -cos (et - 4) + 1 %3D…

A: Given:-   D.E:dydt=et sm et -4                  Initial condition: y ln 4=0   To calculate:…

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A: We can use the trigonometric identity, cos A cos B=12cosA+B+cosA-B . Use the integration formulas,…

Q: Use Table 5.6 to evaluate the following indefinite integrals.∫dx/√(36 - x2)

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

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Q: Use a change of variables or Table toevaluate the following definite integrals.

A: Given:  Calculation:  Let ln(p) = u Differentiate both sides (1/p)dp = du Also the limit of…

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

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Q: y" + y = 3x sin x

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Q: tan x dy +y sin x dr = 0, when x = 0, y = | O y (3- cos 21) = 2 O y (cos 2x O y° (2 – cos 2x) = 1…

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Q: Use a change of variables or Table toevaluate the following definite integrals.

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Q: [10 sin(2x) cos(2x) √ cos²(2x)-5 dx O a. 5 (cos² (2x)-5) ³/5 + C 3 5 O b. -(cos² (2x)-5)³/2 + C OC.…

A: To evaluate the given integral.

Q: Find the area.   y = 3 cos(4x),    y = 3 − 3 cos(4x),    0 ≤ x ≤ π/4

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Q: au at a²u 28. Solve Əx² U(x, 0) = 3 sin 2+x, U(0, t) = 0, U(1, t) = 0. = where 0 0 together with…

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

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Q: What substitution should be used to solve the integral x²dx 4-9x2 sinu=3x/2 O sec u =2x/3 O sec u…

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Q: Solve the given differential euation: dr/dθ+rtanθ=10cosθ. 1.r=(10θ+C)tanθ 2.r=(10θ+C)cosθ…

A: In this question we have to solve the given differential equation.

Q: The integration expression sin(3In(x) + 4)cos(3In(x)+ 4)dx must be transformed into using suitable…

A: topic- indefinite integration

Q: tan 2x – 1 dx. 5 tan 2x + 5 Q5: Determine 1 In |sin 2x + cos 2x| + C 10 A 1 В In |sin x + cos x| +C…

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Q: Use a change of variables or Table toevaluate the following definite integrals.

A: Evaluate: ∫02x316-x4dx            ...(1)

Q: Substitution review Derive integral formula 14 in Table 8.1: tan ax dx = -In|sec ax| + C. a

A: Given: verify that ∫tanaxdx=lnsecxa+c we know that tanθ=sinθcosθ

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

A: We have to evaluate ∫dx1+4x2 Given integral can be written as: ∫dx1+4x2=∫14dx14+x2=14∫dx122+x2 From…

Q: The integration expression sin(3In(x) + 4)cos(3ln(x) + 4)dx must be transformed into using suitable…

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Q: 3. = Cos xsin +xax+a 5/2 3/2 1. Ans: Y= 4sin'x* sinx+ To CAx+4)^- Cax+a) 3.

A: To solve: dydx=cos3x sin2x+x2x+1 Solution Given differential equation can be written as: dy=cos3x…

Q: Use Table to evaluate the following definite integrals.

A: The given integral is: ∫0π16sec24x dx From the table given , ∫sec2ax dx =1atanax +C. ∫0π16sec24x…

Q: Classify and Solve; +9 = cos² t + sin² t + cosh t + sinh t + 3 sin t – 3t dt dt2

A: d2ydt2+9dydt=cos2t+sin2t+cosht+sinht+3sint-3t…

Q: Prove that: cos(nx) - cos(na) cos(x) – cos(a) sin(na) sin(a) dx = n neN, a ER - {0}

A: To solve this question take different values of n and calculate LHS and RHS separately.     if…

Q: Use a change of variables or Table toevaluate the following definite integrals.

A: To evaluate: ∫0π2sin2θ cosθ dθ Solution: Let substitute t=sinθ dtdθ=cosθdt=cosθ dθ Limit will also…

Q: ♥ дzu ахбу = сезх созу, Ans: u(x,y) = sinx siny + x² + 2 cosy - #2² X 1 бу исx;#) =X бx U(x,п) =X,…

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

A: ∫dx36-4x2

Q: 15. ſ sin² 3t cos 3t dt

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Q: Use a change of variables or Table toevaluate the following definite integrals.

A: Since, we have to calculate:-∫-2π2πcos(θ8) dθ -(i)

Q: Use Table to evaluate the following definite integrals.

A: The given integral is ∫0π40cos20xdx   formula used: ∫cosaxdx=1asinax+C

Q: (2x) Sinx 2. Prove that (1) Jy₂ (x)=√√(x) =_ (11) J-y₂(x) = √(3/1²) Cosx

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Q: Use a change of variables or Table toevaluate the following definite integrals.

A: The given integral is ∫04p9+p2dp. Let x2=9+p2. This gives  2x dx=2p dpxdx=pdp. when p =0,  x=3. when…

Q: Show that y1(t) = cos(3t) and y2(t) = sin(3t) are linearly independent for all t

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Q: Integr S√₂-cod -1 ation fuctions. 1-cos²x) dx Not of the above B 1 O

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Q: Find the general solution 6. y"+4y' = sec2x Solution 6. y=c, +c, cos 2x+c, sin 2x+ 16 sin 2x -In(sec…

A: Given differential equation is y'''+4y'=sec2x We have to find the solution of the given differential…

Q: az Use an appropriate form of the chain rule to find dt 1 z = 2 cos x sin xy; y = 5t t Enter the…

A: z=2 cos x-sin xy ; x=1t; y=5t   see z is a function of x and y ,where x and y are functions of t so…

Q: 30 csc (3x) cot(3x) dx (Use Substitution Method) 30 30 + C 6 cos² (3x) 6 30 30 + C 6 sin²(3x) 6 30…

A: Given that  I=∫ 30csc23xcot3xdx We need to substitute the appropriate value so we can solve it…

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A: We have given integral Let, I=∫sinθ2cosθ2sinθdθ As, sin2x=2sinxcosx sinx=2sinx2cosx2 So,…

Q: 1. dz (1² + 5)² 2. COs z dz 3. sin 3r cos 5z de

A: Given: I1=∫x3x2+52dx, I2=∫excosxdx, I3=∫sin3xcos5xdx

Q: e sec(3x+2) sin(3x+2) dx Evaluate cos² (3x+2) -3e sec(3x+2) + . O 1 ,sec(3x+2) + C 3 1 ,sec(3x+2) 3…

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Q: Find the particular solution using the initial condition. y' sin(2y) - cos x = 0, y() = 0 O y = cos…

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Q: ∫0π/2[√(cos3x) sin3xdx]

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Q: Find the solution of the equation zxx + zyy =e-xcos(y) which tends to zero as x-> ∞ and has the…

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

A: Given     ∫(x+1)42xdx Formula ddx(xn )=nxn-1 ∫xndx=xn+1n+1+C

Q: H.co/ prove That;. dz 1-2 Cosh2=

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Q: 1+cos 2x dx sin 2z O cot 2x - csc 2x + c O cot 2z +In |sin 2z|+ c O none of these O In (csc 2x + cot…

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Q: azu Ex: Solve the partial differential equation дудх sin³x cos²y given that du %3D siny when x=0 and…

A: First take x as a constant and integrate with respect to y and the other one