d'y Using method of variation of parameters solve + 4y = 4 tan 2x dx?

Q: 4. Bernoulli's Equation 3dy – 4xy dx = 3x²y*e=2x² dx

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Q: (sech°x)/1+ sin? if y = dx dy Find tanh°x

A: Given:-       To find:- dy/dx

Q: 2. cos“ y sin’ ydy

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Q: aluate 4e3 tan z sec2 x dx.

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Q: and dr= %3D Solve for the differential of y When y=sinxx x

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Q: 17. sech? x tanhx dx 12

A: Integrated by substitutions

Q: Solve d'y dx² cot x dy - sin² sin²x.y - dx = cos x - cos³ 3 OHS X.

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Q: y = [cosh(2x)]ot*( 1 cot-1 3 Vx

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Q: 4(sinh 5. Evaluate 6 x) dx V1+x?

A: We use the well known formula for sinh^-1(x) = ln(x + sqrt(x^2+1)) and then integrate the…

Q: S sin 2x sin 4x dx 7.

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Q: Solve 3e* tan y dx+(1-e*)sec² y dy = 0.

A: To solve the given differenrial equation.

Q: 4. X sin (x) dx VI-X 1-メ-

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

Q: 28. Se cost sin 2t dt

A: ∫0πecostsin2tdtSolution :∫0πecostsin2tdt2∫0πecostsintcostdtlet, cost=x-sintdx=dxsintdx=-dxat…

Q: olve the equation on the interval 0s0<2x V2 sin0- sin 0 = 0

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Q: 3. dx (sinh(2xV1+x du

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Q: 1. S sinh ) dx 2. S sech? (x - ) dx 3. [6 cosh (- Inx )-) dx

A: Since you have posted multiple subparts question in this question so I have solved first question as…

Q: Li S cos(x)esin(x)-2y dxdy

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Q: a) Find for 5x² – x³ sin y + 5e*y = 10 dx

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Q: (#6) S sin³ (x)dx =

A: Given  Rewrite  sin3x=  sin2x * sinx  Use Pythagorean identity sin2x + cos2x=1

Q: S sin(4x + 3)cos(3x – 5)dx -

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Q: 3. S sin x sec®x dx

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Q: 2- Solve the equation for x : Cosh x = Sinh x +1/2.

A: We need to find out the value of x. The given equation is Cosh x=Sinh x+12 Now,  Cosh x=ex+e-x2  and…

Q: Using dx/dy solve sin(x+y)-cos(x+y)=1

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Q: solve sin2x dy/dx-y=tan x

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Q: Tutorial 14 If y = (sin-1 x)², show that dy (1 – a²) - dy = 2. dx dx?

A: Given, y=sin-1x2 Differentiate with respect to x y'=2sin-1xddxsin-1x=2sin-1x11-x2y'=dydx=2sin-1x1-x2…

Q: "/2 cost x dx "/4 sin6 x

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Q: S(sin 29x + 6e0 +5 cos 5x+)dx

A: Given integration ∫sin29x-x5+6e6x+5cos5x+x5dx  Now we break it and we get   ∫sin29xdx-…

Q: 05 (show resulting de) dy x sin x dx cscy

A: Given; dy/dx = x2sinx/cscy.

Q: (dy/dx)tan x sin 2y = sin^2(x) + cos^2(y) differential equation

A: Solution is here

Q: Solve (1 + y) dx = (tanly-x) dy

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Q: olve dy/dx+y=cosx-sinx

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Q: Solve sin - () 2 dy = x + y

A: We need to use substitution method to solve this differential equation

Q: [17 sin³ x costx dx 5.

A: Given: I=∫17sin3xcos4x dx. To evaluate: Value of integral I.

Q: lel sin(mx) sin(nx)dx=0 (a)

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: solve sin2x dy -y=tanx dx

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Q: Solve d²y cot x dx² dy - sin² dx sin²x.y = cos x - cos³

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Q: 2e3* sin 2x dx

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Q: ) y= tanx+ sin x 0<x<27 (k) y=sinx -2n Sx< 2n

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Q: 1 y = [cosh(2x)]°or¯*( cot-1 3 VX

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Q: Solve: COS x y'dy +ye' sin x dx = 0.

A: The detailed solution of the problem is given in the next step.

Q: X= sin 2tS In %3D Find dw 2- Cost

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Q: Jam sin(10x) dx

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Q: I. Power Formula cosh3x dx 1. S (1+2sinh3x)5 tanx dx 2. S (1+Iпcosx)2 3

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Q: 4. EVALVATE | sin4x vos5x dx

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Q: Find dy/dx by implicit differentiation. 11 11 dy/dx = (Express your answer using positive exponents…

A: The given function is 11x3+11y3=7

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

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Q: cos x dx Sx x sinx cosx dx 4. 3.

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Q: dy + y - Sin X dx =0 difference Ekact Solve.equation by

A: The objective of the question is solve the equation of difference.

Q: S sin(v3x + 2}dx

A: To evaluate the given integral

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.