d²x + 16x = 1 + 2 sin 4t dt2 dx (0) = 0 x(0) = 0, %3D dt

Q: An Integration factor of this differential equation is .7 3x? + 1 + x3 dy 1 y : 1+ x2 dx

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Q: dx (2) S V9-x² E(Ctrl) X. 2x sin-1(구)+ sin-1 (민 + Option 1 Option 2 2x cos-1(민 + c CoS Option 3

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Q: What is the integrating factor for the linear differential equation 2(y - 4x^2) dx + x dy = 0?.

A: Given:  2(y - 4x^2) dx + x dy = 0

Q: sinx dy = 0 y cos xdx + 1+

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Q: dy sin x 3) dx y=2cos sin x- 1 of first order linear differential equation COSx COsx y(7/4) = 3/2…

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Q: 1. [ (6x² – 2x+3)dx sin(2x)dx 3 2. 3. S2 8 dx X+2

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Q: 1. S(7x³ + 4x²)dx e*dx 2. J itez* 1+e2x 3. S(V1 – cos x)dx

A: We will these indefinite integrals as

Q: Use integration to find a general solution of the differential equation.

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Q: What is the general solution to the differential equation (3 tan x – 2 cos y) sec?x dx + tan x sin y…

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Q: S sin (2x – 1)cos (2x-1)dx (2х - 1)dx

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Q: Use integration to find a general solution of the differential equation       dy/dx = (6 − x)/3x , x…

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Q: Use integration to find a general solution of the differential equation                  dy/dx =…

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

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Q: Use a technique of integration or a substitution to find an explicit solution of the given…

A: Cross multiply first to take x terms on a side and y terms on another side. Then integrate both…

Q: 2 (b) - 2y dx +(2y tan'(x )-2x +sinh (y))dy = 0

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Q: e2x dx 1. Зе2x+1 2. sinx dx 1 3. cos 2x

A: As per bartleby guidelines we are supported to answer only first three subparts,  kindly repost…

Q: (ylny-exy)dx + ( + xlny) dy = 0

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Q: dx (2tx +x+ cos t) + (-sin x +t² +t)- = 0. dt %3D

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Q: 1. ſx² e*³ Sx² e**dx 2. cos'xsinxdx sin3xsin 2x dx 3.

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Q: Use Exact Differential method ( Rule II) to solve : (x² – y²)dy = xy dx.

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Q: (cos 2y – 3x²y²)dx + (cos 2y – 2x sin 2y – 2x³y)dy = 0

A: We will find out the required solution.

Q: dy +cosh 2y=0 dx 3. sin x ans: sinh 2y-2cosx3Dc

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Q: | (3x – 2x + 1) dx 5. |(x - 1)° dx 6. 7. (x² – x*) dx 8. cos x dx /2 I sec' x dx 9. dx 11. (4 – 2x')…

A: 5. I=∫13(3x2-2x+1)dx =∫133x2dx-∫132xdx+∫13dx =3∫13x2dx-2∫13xdx+∫13dx =3x3313-2x2213+x13…

Q: Use a technique of integration or a substitution to find an explicit solution of the given…

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Q: ACTÍVITY 2: Differentiate the 1) y = -2 sin 2) s (t) = - WE

A: Apply the differentiation rules for the trigonometric functions to get the derivatives of the given…

Q: dx +4x = 2e 3 , x(0)= 5 dt (d) dx +4x = sin 2t , x(0)= 0 dt (e)

A: Laplace transferom, solve the differential equation by using Laplace transferom

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: Integrate: ∫ 3cos(2πx) dx

A: The given integral is ∫ 3cos2πxdx.

Q: Find the integrating factor: cos⁡ x dy+[(y sin⁡x )-1]dx=0

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Q: A/ Integrate TWO only 2x dx 1) S- 2) S 4e cos4x dx 3) x In(x + x)dx x +x+1 B/ Ali is filling a cone…

A: As per the guidelines we can solve 2 problems

Q: Use a technique of integration or a substitution to find an explicit solution of the given…

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Q: +(g-1)dx -t +(2xy-Siny]dy=o

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Q: dy COS X + y sin x = sec² x dx solution of above differential equation is

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Q: Use integration to find a general solution of the differential equation                  dy /dx = x…

A: Given: dydx=x1+x2 Multiply both sides by dx dy=x1+x2dx

Q: zln x dx 2) S 3 cos3 x sinó x dx 3) 12.1 dt 13. 3t + 2

A: Explanation of the answer is as follows

Q: tan(4x + 8). Find the differential dy when x = Let y 1 and dæx 0.3 Find the differential dy when x =…

A: In the given question we have to find dy of the function at both of the given value.

Q: dy/dx+(sinx/cosx)y=2cos^2sinx-1/cosx of first order linear differential equation y(pi/4) = 3√2 find…

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Q: Show that the sine integral satisfiesthe (differential) equation xS'(x) + 2S''(x) + xS'''(x) = 0.

A: Given information: Sx=∫0xsinttdt To prove xS'x+2S"x+xS'''x=0

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

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Q: dx 25. Integrate: S Ve-2x –1 А. Sec-1e* + С В. Sec-1е-* + С С. — Sec-1e* + С | D. —Sec-1e-* + с

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Q: 2) / vĩ IneF dx dx etan x dt dx dx 3) 1- sin?x 4) t In vt 5) J Jx (1 + x)

A: Here, we need to find the value of the integration  1) ∫x+35xdx 2) ∫xlnexdx 3) ∫etan(x)1-sin2xdx

Q: dt dx 3. 6x – x² 4. sin xV1 XN Cos xdx 3x 5. 1-2e3*) 6. dx

A: We solve only 4th question.  Let 1-cos(x) =t

Q: dæ + 2x +5/ x dt = 1 1 where: x (0) =0 dt

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Q: Use integration to find a general solution of the differential equation                      dy/dx =…

A: Given the differential equation is   dydx = 2x(4x2 + 1).   dy =  2x(4x2 + 1)  dx Integrating on the…

Q: sin 6x dx sin23x 4. 6. S Ve3x + e 4x dx ex dx 8. J 1+ e2x

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Q: Find the particular solution of the differential equation (1-cos(2t))dy/dt=xsin(2t) given that…

A: The given differential equation is 1-cos2t dxdt=x sin2t     with xπ2=2. Solve as follows. 1-cos2t…

Q: dx b) sin 2x sin x dx (3x + 2)²

A: we have to integrate

Q: 1. S(e2x – 1)3 dx 3. S sin 2x (sin®x + 1) dx 2. S(x6 – 3x²)ª (x5 – x) dx -

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Q: tan-1 (xy)=3x2+sin-1(y) find dy/dt

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Q: 2 1) (-2xy) dx + (Siny-x²) dy

A: see my solutions