y" +y' = cos 3x

Q: find the integrating factor of cos(x)y'+sin (x)y=2cos^3(x)sin(x)-1

A:

Q: Find the value df (a) that Make ECX) is Contincity at X- Ž

A: Given that :f(x)=cosx2x-π      ,             x≠012a2-3a+4      ,   x=0

Q: Describe the method used to integrate sin" x cos" x, for m even and n odd.

A: The method to integrate sinm x cosn x when m is even and n is odd. We integrate by substituting the…

Q: Suppose that y = 4 cos² t , x = v3 sin(2t) and 0 < t<a. Then dt2

A:

Q: evaluate using Integration by Parts.

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Q: 2x cos(2x)dx

A: Given : ∫2xcos2xdx

Q: integrate t2 sin(2t) dt from 0 to 8pi

A: We will  Integrate by parts using the formula:              ∫u v dx = u∫v dx −∫u' (∫v dx) dx.

Q: Determine of y = cos(x) – V5a2 In x.

A: I have stated the used formulas in the solution.

Q: Find the general solution to the ODE using the method of Variation of Parameters: y" + y= cos² x

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Q: Evaluate cos √6x dx using a substitution followed by integration by parts.

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Q: use the chain rule to find: 28) dv 2- COSxy + y cos x

A: Solution:Given   z= cos xy+ y cos xx=u2+v and y=u-v2To find :dzdvFormula:ddx(cos x)=-sin…

Q: dx S COsxtanx

A: Here we will solve the given integration,

Q: Ssin(2x+3)dx= d -1 cos(2.x+ 3)+C 2 a 5 cos(2.x + 3)+C -1 cos(2x+3)+C - cos(2x+3)+ C e cos(2x +3)+ C

A:

Q: Find integral.

A: We have to find the integral I=∫cos(5x) dx

Q: Solve exact equation 2x -)dx + (2x cos(2xy) + 8e²")dy = 0 x² + 1 (2y cos(2ry) + with initial…

A: We will solve the problem.

Q: Differentiate : a. y= 9x sec (x/3) b. y= sin2x/1-cos2x

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Q: y 2sin x-cos 2.x for 0° sxs360

A: Consider the function, y=2sinx-cos2x Differentiate with respect of x,…

Q: solve the IVP x(1-siny)dy=(cosx-cosy-y)dx y(π/2) =0

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Q: What is an integrating factor of the nonexact DE  (2y^2 + 3x) dx + xydy = 0 ?

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Q: Verify the integration formulas ∫sech x dx = tan-1 (sinh x) + C

A: To evaluate ∫sech x dx

Q: What is the integrating factor of (y – cos² x) dx + cos xdy = 0?

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Q: Find the solution of (tan x – sin æsiny) dæ +cos xcosydy = 0

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Q: 5

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Q: Solve for Txyz given the function T(x, y, z) = z tan (In x - √y)

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Q: y" + 2y' = sin 2x ||

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Q: dy cosx+ ysin x =1 dx

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Q: Ssin (2x)cos(2r)dx

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Q: Find the solution of the equation in the interval 0"sx <360 1. cos x+) 3 = - cos x +T3%3D

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Q: Solve the initial value DE y' - ytanx = sinx, y(0) = 1 5-cos 2x 5-cos 3x 5-c A) y B) y = с) у %3D 4…

A: Given differential equation is y'-ytanx=sinx,   y0=1 Compare the given differential equation with…

Q: Describe the method used to integrate sinm x cosn x, for m even and n odd.

A: Method to integrate sinmx cosnx ,for m even and n odd. Let m=2k and n=2k+1 ∫sinmxcosnx…

Q: Cos 5x dx 3 +Sin 5x 1. 2. dx J16-9 (n x)²

A:

Q: Find dy/dx for 4 cos4 xsiny = 15

A: d(uv)dx=udvdx+dudxv

Q: Ssin^3 (2/3 x) cos^4 (2/3 x) dx

A:

Q: (a) Determine f 2xe3*dx by using integration by parts. (b) Determine S cos(x²) 2x dx by using…

A: Given,  ∫2xe3xdx ; We have to integrate using integration by parts ∫cosx22xdx ; We have to…

Q: Find the solution of the DE using reduction Order (D2 + 4)y = sinx

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Q: Use the method of undetermined co – efficient to solve: y'' + 2y = sin (x)

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Q: S" cos de 4. 2 dx .2 -1 1+x² 5.

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Q: solve using homogenous and exact. (2x-3y)dx+(2y-3x)dy=0

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Q: valuate f¹² Vsin x + 1 cos x dx.

A: Topic:- application of integration

Q: 2. Use integration by parts to solve for [x³c x³ cosx dx.

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Q: Intergrate dy (2y-x) =In Co)

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Q: Integrate using substitution: [x* cos(x' )dx

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Q: Use integration by parts to verify the reduction formula.

A: We have to verify the reduction formula using integration by parts, ∫cosn x dx=cosn-1 x sin…

Q: Integrate by parts f(x)=sin4(x)cos3 (x) dx

A: Given the integral  I = ∫cos3(x) sin4(x) dx cos2(x)=1−sin2(x) I = =∫cos(x)(−sin4(x)(sin2(x)−1)) dx…

Q: f(x csc² 2x - x cos 2x)dx

A: The given integral is ∫xcsc22x-xcos2xdx. The objective is to solve the given integral. Following…

Q: 2. f x cos² x dx

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Q: Use a linear approximation of f(x)=cos(x) at x=5π/4 to approximate cos(222∘)

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Q: Differentiate implicitly for the equation for x^2y+x^3-cos(x)=3y^2

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Q: dy - 1 = siny dx

A: Given : dydx-1=siny To Find : solution of Given DE