Q3/ Find dy for the following functions: (choose only five) dx 1) y = (x² + 1)5 2) ху + 2х — 5у - 2 3) у 3D In(x - 5 хЭ) 4) y = [In(x²+2)²]* %3D 5) y = 7*2 6) y = log10 2x

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

A: The solution is given as

Q: 4 If y = x, then F z = log.y G y = log,z H x = logry z = log,x

A:

Q: 3. Find syz for ys = In(x + yz) – xcoth-1 log ().

A: Given : Let us consider the given value as,  ys=ln(x+yz)-xcoth-1logzy

Q: 8. In V5x 3 y z2 9. log. V xt 10. loga Va b5

A:

Q: 6. More models For each of the models listed below, predict y when x = 2. a) ŷ = 1.2 + 0.8 log x d)…

A:

Q: The solution of the following logistic equation is dy = ry dt (13-): (0)- k 10

A:

Q: Find if z = log2 y – 6 log5 y. dy dz dz In- dy y In 10 dy y ln 10 Option 1 Option 4 64 dz In- 64 dz…

A: We know, ddxlogax = 1x·ln a a·ln b = ln ba ln a - ln b = ln ab

Q: 1) Find dy/dt for if : y = log2 (87ln 2)

A: Apply differential rule to solve 1st question [ln(u(x))]'=1u(x)u'(x) power rule [x(n)]'=nxn-1 Apply…

Q: in The solution of the equation Log(z² – 1) = is %3D Select one: 1 in 1 19T 22e 8 and 22e 8 1 in 1…

A:

Q: The solution of the following logistic equation is dy = ry (11 –):y (0) = k %3D dt 13 1 ellrt 144 Y…

A:

Q: dw Find if w = x10 + 10*. dx log 10 dw dw 10 10x° + 10* 10x° dx dx log10e O Option 3 O Option 1 dw…

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

Q: dz dz +y дх = 50 +x4°y+y5° ), Prove that x ду If z= log (x50

A:

Q: Find the general solution of the logistic equation *- » dy dt = 3y (1 -) n find the particular…

A:

Q: а. (у + 2)2— 2x log y - In u = 2e-x, k > 0 ay ax? ду? b. uxx + xy uxy + y²u² = 0 = v2 + x azu C. t-…

A:

Q: Solve ylogydx + (x- logy)dy = 0.

A:

Q: 19. If logx y + log, x = 2.9 and xy = 128, find x + y. 24 O 20V2 O 36 O 34V 2 O 66

A:

Q: The number N(t) of people in a community who are exposed to a particular advertisement is governed…

A: Given that Nt represents the number of people who are exposed to a particular advertisement. The…

Q: (i) Show that the solution of the logistic equation dr az – br dt (3) is given by 1(t) a – br(t)…

A:

Q: 4) Find the singular points, residual values, ond of +he = (2 function,

A: The given function is f(z)=1(z2+2z+2)3 The singular points are the points where the denominator of…

Q: Find ay dx 3. 4. 5. y = 2e³x5tanhx y = xln(5x-2) y = sec ¹(log 7x)

A: Given :y=2e3x5tanhx4. y=xln(5x-2)5.  y=sec-1log7x

Q: 1) Find dy/dt for if : y = log2 (81'n 2)

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

Q: Find the solution of the initial value problem y" + 2y' + 10y = 0, (7) = 0, y () Y y(t) = = = = 12.…

A:

Q: Find the solution of the given initial value problem. 5y""+65y-580y = 0; 11, y'(0) = 31, y"(0) =…

A: A detailed solution is given below.

Q: B. Express as a single logarithm and, if possible, simplify. 1. log, x + 4 loga y – 3 loga x 6.…

A: This is a problem related to logarithm properties. Based on the general formula we can answer the…

Q: write the logarithmic equations in exponential form.

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

Q: [E] Prove with usual notations that (i) hD = log(1 +A) = – log(1 – V) = sinh '(u8)

A: We will prove the following result.

Q: 14. Find the domain of definition of the function 31 Vx + 5 X-5 y = log10 (,2 x² – 10x +24

A: The domain of a function is the set of input or argument values for which the function is real and…

Q: 2. If the rate of transmission of an additional case of covid-19 is 0.3 per day starting February…

A:

Q: dy Solve the initial-value problem for y as a function of r. (4 x) = 1, y(0) = 4 de…

A: Given initial value problem is,

Q: Find the solution of the initial value problem y" + 4y' + 5y = 0, Y (²7) = 0, y¹ (7) у y(t): = = 6.…

A:

Q: The solution of the following logistic equation is dy - ry (7 –);y(0) k dt 15 1 -e7rt 105 y – 7k 1…

A: Given

Q: - y =log x² dy_ 8log, x A. dx dy 4log, x В. dx dy _ 4xlog, x xIn 2 dy 8x log, x D. dx xln2 xIn2 dx…

A:

Q: 2) y= log, (-4x +6)+ 4 2 +6 1) у3D 4) y= In (4x – 10) – 6 e+10 3) y =

A: SOLUTION- Since you have posted a question with multiple subpart , we will solve first three for you…

Q: 13. Integrate the following: a. b. (3-7x)6+ log 4 (2x - 5) 27 9 + 2x [ 74X_ cos(1 + 3x) + - + dx 5…

A: To evaluate give integration.

Q: Find the solution of the initial value problem y" + 6y' + 10y = 0, Y (²7) = 0, y¹ (7) = 9. 2 y(t) =…

A:

Q: Express the following in terms of x without logs or natural logs 1) log100x 2) 1000logx 3)…

A:

Q: Differentiate y = (9x- 11) log3 (1læ – 9). %3D A. y' = 9(11x-9)+11(9z-11) In(9r-11) (9x-11) In(3)…

A:

Q: 6) If u = log (x² + y²), then prove that log (x² CSScanned with CamScanner dydx ôxôy

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Q: Find the greatest integer less than or equal to log29 S² log2 (x³ + 1) dx + (2x - 1)³ dx.

A: At first, we have to evaluate: I=∫12log2x3+1dx + ∫1log29(2x-1)13dx

Q: Differentiate y = 3e +7 ln(2x) + log, x- 4" O y' = 15e5 ++ 1 - 4* In 4 %3D - I In 2 O y' = 15e5-1 1…

A: We have to differentiate  y = 3e5x + 7 ln(2x) + log2x - 4x.

Q: It is expected in traditional mathematics that when you input data into a well-defined equation you…

A: As per the question we are given the logistic equation : xn+1 = f(xn) = rxn(1-xn) And we have to…

Q: 4. Solve for x: a. 100(1.04)²x = 300 b. 2+ log v1+ x + 3 log VT–x = log v1 – x² c. V35x-I = 9 d.…

A:

Q: 14.3. EXERCISES 207 a, y, z > 0. b) log(Vr² - Vy7)

A: The objective is to simplify the given expression

Q: B. Express as a single logarithm and, if possible, simplify. 1. log, x + 4 loga y - 3 log, x 6.…

A: According to our company's guidelines I can only answer first three subparts of the question B since…

Q: 3. Find syz for ys = In(x + yz) – xcoth- log ()-

A:

Q: Find w if w = x10 + 10*. dx 10* 10x° + In 10 log10 e dw dw 10x° + 10* dx dx Option 2 Option 3 In 10…

A: Given  w=x10+10x To find : dwdx

Q: d log, x = 1 dx [(In a)(x)]

A:

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.