6. + 6x) + (In x - 2)y' = 0

Q: dy/dx if y=tan((1-2x)/(1+x)) dy/dx if y=x^4 ln(3x-1)

A: 1)    y=tan1-2x1+x2)    y=x4ln(3x-1) Hint:  Chain rule and then uv and u/v rule of differentiation

Q: 3. (4x³y5 sin 3x + 3x*y$ cos 3x) dx + 5x*y* sin 3x dy = 0 y(0) = 1

A:

Q: 7. Evaluate Soy4 2 - y dy using Gamma/Beta function.

A: The solution is given as

Q: The general series solution about the ordinary polnt 0 of the differential equation y"+x²y 0 is:…

A:

Q: (1) y = x³ lnx (4) y=²+1 (2) y = √sinh √tan.x -,u= u= 3x²-2

A:

Q: How would I approach this problem algebraically, and analytically? I have attached a photo.

A: To find:

Q: (1) Find the general solution for -) dx - -) dy = %3D

A:

Q: (2y-1 + cos 3z) 분. 4x3 + 3y sin 3x = 0 (1)

A: We know that if - M(dy/dx)+N=0 Then M(dy/dx)= -N Therefore- dy/dx= -(N/M)

Q: 5 Find xy dydx. 4

A:

Q: 3-S- In(x²+x)-Inx-elnx dx In(ex+1))

A: We will be using the integral formula of log function to solve the above given integral. We can…

Q: 2). 3rin y l dy dx [ 5 X In Xナ3

A:

Q: 2. Show that P(1-x)° dx= x'(1-x) dx. %3D 0/

A:

Q: 1. Ye = cost- sec(at) %3D ans: =-2sin t - asec(at) tan(at)

A:

Q: 2 iii. sech x3 tanh( x3 S- -dx 1 X3

A:

Q: 4. Integrate COs x dx

A:

Q: first and second derrivative of: y=Arccos(e^2x)

A:

Q: 5 sin“(3t) dt

A:

Q: ind dy/dx if y=8x-3/24x^5

A:

Q: 25. Find x, y, eR from 2coshy - 7sinhx = 3 and coshy - 3 sinh² = 2 %3D

A: The given system of equation: 2cosh(y)-7sinh(x)=3                    ......  (1)cosh(y)-3sinh(x)=2…

Q: 13. To evaluate S - 3cos²x=1 dx, the integrand can be transformed to 1-sin²x a. [(3cos³x+ csc²x)dx…

A:

Q: 2 L sinh–t|= 3 6. 9s2 – 4 3 2s2-4 6. s² – 4 - 3s2 – 4

A:

Q: 2 1 Estimate -dx using the right endpoint rule with n = 4 3 1+x

A:

Q: If UX = 6 and XY = 5 solve for UV. Round to the nearest %3D %3D hundredth. U

A:

Q: (2(1-2) (1--) dy dx dz 1-z) Evaluate S, a-2 (1-

A:

Q: - ((x3 + x)sech(In x)) = dx EX)-

A: To find  ddx(x3+x)(sech(ln x) We use product rule  d(uv)=udv+vdu Let  u=x3+x,     v=sech(ln…

Q: 5. 2x sinh+ 3y cosh2) dx -- 3x cosh dy = 0

A:

Q: 1- S7 cos(y)eSin(y)+9X dydx

A:

Q: 2 sinh 3x cosh 2y dx + 3 cosh 3x sinh 2y dy = 0

A: We know sinh xcosh x = tanh x ∫tanh ax dx = 1alncosh ax + C    (where C is constant of integration)

Q: 7. Integrate em***)dx_using the Substitution method. x +3

A: To evaluate the given integral using substitution method.

Q: -) Solve the following partial differential equation us ing direct integration: a²u = cos (x +y) дх…

A: Topic:- application of integration

Q: 11. Find the length of the curve x = on the interval (2, 4] (integrate with respect to y) 12y3 un

A: Given that the function x =y55+112y3 Find the arc length of the graph of the given curve on the…

Q: Find the differential of the given functions. 1. y= x-2x² + 5 5. у 3 1- -s2

A:

Q: uxiliary equation of + by = 0 are re tion of the different

A:

Q: 5) Form a DE by eliminating the arbitrary constants from the equation y = asin(4x + 1).

A:

Q: Find a result by using homogenous for (x³ - 3x²y)dx-(x3³ - y³)dy = 0

A: This question is based on solution of Homogeneous differential equation.

Q: 11 Show that dy dx = 1-In2. 8(xy +1) 0 0

A: Follow next step

Q: 1 J sec- ztan - zdz

A: Solve the following

Q: Find dy/dx 1. y = sin ( 5x - 9) 2. y = sin-4x/5

A:

Q: 4. You will need to use L'Hopitals Rule in this one Sxe-* dx

A: This is a improper integral problem

Q: 22. Find OY if y2 - 4xy + x² = 10. dx

A:

Q: find dy/dx of y=sin^2 4x+1/2 cos 8x

A: Given,         y=sin24x+12cos8x

Q: 2) Integrate: S(29sinx + 6e + 5 cos x + Vx)dx

A: Given that, The integral ∫29 sinx +6ex +5 cosx+x5 dx By using ∫f(x)+g(x)dx =∫f(x) dx +∫g(x) dx ∫ 29…

Q: 1-f²₁ ¹/²(y² sinx dx dy) 2-√²-dxx2 0 3- f(cscx cotx)² 2 4- f₁² x (x − 3)dx for 5-S²₂ (x³ + √x) dx

A: 1.

Q: 17. Show that V10x + 1 and Vx + 1 grow at the same rate_ as x→o by showing that they both grow at…

A:

Q: 4. Find derivatice y 4=In (x 3-4x²+1)

A:

Q: Evaluate the integrals

A: Given integral is:

Q: 2-S S dx dy

A: to find the double integral we consider a strip parallel to x axis

Q: 2. ху 4 a. when x=8 10 dx b. when x-1 dt dy dt -6

A:

Q: Find the differential equation of all family of circles with center at the line 3y - x = 0 with h…

A: