Find y' and y". - in(x + V6+ x²) y = In( x + y' = y" %3D

Q: y(ln x – In y) dx = (x ln x – x In y – y) dy %3D - -

A: This is the question of differential equations.

Q: [3tan(x)² dx 2

A: Concept: Integration: The Sum of discrete data is denoted by Integration. The integral is calculated…

Q: 4 Inx b) Evaluate x'dydx by first reversing the order of integration.

A: Solution Given ∫04∫0ln xx2dy dxwe need to evaluate by first revesing the oder of integration

Q: Solve using integrating factor by inspection: (x^3+xy^2-y)dx+(y^3+x^2y+x)dy=0

A: Solve using integrating factor by inspection: (x^3+xy^2-y)dx+(y^3+x^2y+x)dy=0

Q: Ssin" x 14 x cos' x dx Integrate:

A: Given,        ∫sin14xcos5xdx

Q: 9 dx dy +ytanhx= 2 sinh x dy - 2y = x' cos x 10 x dx

A:

Q: Integration by parts with u = ln x, dv = xdx

A: u=lnxdv=x dx

Q: S2x²e** ax=uv- Jvau -Svau. Sfoxe". Using Integration By Parts, Find uv- Jv du- 3 x² e dx O 2 x3 x3…

A:

Q: x2 dy dx by reversing the order of integration. 4/x 1. Evaluate

A: Given double integral is∫14 ∫4x4x2 dy dxNow , By interchanging the integral we have ,∫y=14…

Q: determination

A:

Q: The exact differential of excos y

A:

Q: find dy/dx

A:

Q: 5. (x2 + y² + 1)dx + x(x – 2y)dy = 0, x = 2,y = 3 %3D

A:

Q: 8. y dx + 2(y -x) dy = 0

A: Linear differential equation in x.

Q: ind the general solution using Integrating Factors Found by Inspection y(x^2 y

A: Given: To find the general solution of By using integrating factors,

Q: Make an octave code to integrate ex with respect to dx from 0 to 1, by Simpson’s ⅓ rule. Divide the…

A: Equation is f(x)=exThe value of the table for x and y x 0 0.25 0.5 0.75 1 y 1 1.284 1.6487…

Q: 3. Determination of integrating factors: 2y(x+ y+ 2)dx + (y -x -4x-1y = 0

A:

Q: 1. S ( cos(2x-1) dx (Integration by Parts) et

A:

Q: Find dy/dx by implicit differentiation. (1/x^3) + (1/y^3) = 4 dy/dx =

A: Given function (1/x^3) + (1/y^3) = 4  We need to find dy/dx using  implicit differentiation

Q: Use integration by parts to show )dy.

A:

Q: In 2x dx 3.

A: We have to find solution

Q: Find the area of the surface formed by revolving y = x³ on 0 < x<1 around the x-axis. Show all steps…

A:

Q: 3. Determination of integrating factors: 2y(x+ y+2)dx +(y² - x² -4x-1)dy = 0

A: The given differential equation is  2y(x+y+2)dx+(y2-x2-4x-1) dy=0. Repost the next question.

Q: differentiatin, detamina dy of ; dx y= [at) (Xts) (a-z) (x-+)

A:

Q: Find /- tan- x -dx using integration by parts. x2 ITM

A:

Q: (x² cosh(sin(x-y))= intx-vn) = X' dy 9.

A:

Q: dy - cosh x dx + (sinh x)y = e¬x

A: see the details solution in below

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

A:

Q: Solve by integrating factors found by inspection: y (x2 - y2 + 1)dx - x (x2 - y2 - 1) dy = 0

A: To solve: y(x2 - y2 + 1)dx - x(x2 - y2 - 1)dy = 0 ⇒yx2 dx- y3 dx+ y dx - x3dy +xy2dy +xdy = 0

Q: A cylindrical shell has a thickness of 0.2 cm. Using differentials, approximate the volume of the…

A: Solution.

Q: Find the integrating factor: x^2 dy+(2x^3 y-e^x )dx=0

A: First order linear differential equation of the form dydx+P(x)y=Q(x) Integrating Factor:…

Q: (a) Evaluate xe* dx using substitution method. (b) Evaluate | 6xe* dx using integration by part…

A: We will find out the required value.

Q: find the integrating factor of (y² - x ) dx + 2ydy = 0

A:

Q: Find the differential of the function. y = 1 divided by x^7 - 8x dy =

A: we have to find dy

Q: THE AREA BETWEEN THE CURVES 4 y = x²³² AND y ²³ = 4X IS REVOLED 2 ABOUT THE LINE X= -1. SOLVE FOR…

A:

Q: 4. x(x² – y² – x)dx – y(x² – y²)dy = 0, y(2) = 0

A: For the solution follow the next step.

Q: What is the integrating factor y(4x+y)day - 2(x^2-y)dx = 0

A:

Q: Find the integrating factor: (2x^2+y)dx+(x^2 y-x)dy=0

A:

Q: 6. Carefully interchange the order of integration to evaluate os(x/²) dx dy. COS -1

A: To evaluate: ∫-11∫y21cos(x3/2)dxdy by changing order of integration.

Q: 1. siny dx + (x - sin² y)dy=0 2. x + ( 1+x)y = e -× sin2x dx

A:

Q: 1. y(x³ – y)dx – x(x³ + y)dy = 0

A:

Q: Se²(x² + 2x dx by using the integration by parts. Q4 Evaluate ,2x

A:

Q: Determination of Integrating Factor (2xy− y^2 + y)dx+ (3x^2− 4xy+ 3x)dy = 0

A:

Q: 9. S sec 2x dx 10. S cos x esin x dx 11. dx x+1

A: Evaluation of the above integration is

Q: sinh x – 1 dx cosh x

A: The given integral,        ∫sinhx-1coshxdx

Q: integral of (2y-3x)dy and integral of (2x-3y)dx

A: We have to find the integrals of (2y-3x)dy and (2x-3y)dx seperately. Recall that the integration of…

Q: Find the integrating factor μ(x) of y' + 4y - tan(x) = 0 such that μ(0) = 1. μ(x) =

A: See the details solution in below

Q: 34. e4x cos 2x dx

A: Solution:Given∫ e4x cos 2x dxFormula:∫udv=uv-∫vdu∫sin ax dx=-cos axa+C∫cos ax dx=-sin axa+C∫eax…

Q: .2 dy Find for y dx V6 – x5 - dy %3D dx

A: We have to find dydx