(a) Find y' by solving the equation for y and d (b) Find y' by implicit differentiation. (c) Check that the derivatives in (a) and (b) ar 1. =D1 2. z² + y³ = 4

Q: What is the general solution to the differential equation (tan x)dy - (4y In y - y tan³x)sec²x dx =…

A:

Q: The rate of change of the height h(t) of water in a cylindrical tank with a hole in the bottom is…

A:

Q: Find the differential equation corresponding to y=a cos (logx) +b sin(logx) or y=A sin (logx)…

A:

Q: Solve the differential equation using variation of parameters. d’y +y= sec³(x) dx

A:

Q: From the differential equation by elimanating he arbitary function f from xyz=f(x2+y2+z2)

A:

Q: diy in terms of x and y. dz² ニ 86

A:

Q: Find an energy function for the differential equation y"=-y3

A:

Q: Find a function of the differential equation: y = x²-2 sin x

A:

Q: y = Ce * + C2e 2x + C3e * + e 2x

A: y=c1e-x+c2e-2x+c3e-x+e2xy=c1+c3e-x+c2e-2x+e2x Here, complimentary solution is  y=c1+c3e-x+c2e-2x…

Q: Find the differential equation of straight lines with slope and x –intercept equal.

A: Recall:  The equation of straight line is y=mx+b where, m=slope, b=y-intecept   Given, slope and x…

Q: What is the differential equation obtained by eliminating the parameter A from the relation…

A: The explanation of answer as follows

Q: Find the derivatives of the functions y = ln (sin2 θ)

A: Given equation:

Q: Solve the differential equation by variation of parameteres: y'' + y = sec(x) + tan(x)

A:

Q: Obtain the differential equation associated with the given non-derivative equation in x and y. Show…

A:

Q: Find the derivatives of the functions y = ln cos-1 x

A: The given function is y=lncos-1x.

Q: dy 8 x2- y2 +2(e¬* – e') = C, dx X -e-* y+ey

A:

Q: in differentials of functions, if x change by a small amount dx then, what will happen to y?

A: Let a function be y=fx then here y is the dependent variable and x is the independent variable. The…

Q: a differential equation is classified as a homogeneous DE if one can directly isolate all functions…

A: A differential equation is classified as a homogeneous DE if one can directly isolate all functions…

Q: Find the general solution of the differential equation y′ = √(tan x) sec4 x

A: The function is y'=tan xsec4x. To find the general solution, integrate both sides of the equation.…

Q: Find the 3rd derivative of (1 + 2y)³ + eª (sin² y) - 3y cos(e=? )

A: Given data (1+2y)3+ex(sin2y-ycosex2=3y and find 3rd derivative or d3dx3=?

Q: Find y2 for differential equation if yI is given: ху" — 20у'%3D 0 Y1 = 15x13 -

A:

Q: Find the point on the curve y = x3 – 3x for which the tangent line is parallel to the x-axis.

A:

Q: The function y(x) is defined by the implicit equation x2−√ylny=1. Find its differential at the point…

A: Differentiate both sides with respect to x and solve for dy/dx

Q: find the derivatives of y=sin(ln|2x+1|)

A: y=sinln2x+1

Q: Obtain the differential equation associated with the given non-derivative equation in x and y. y =…

A: Given that obtain the differential equation associated with the given non-derivative equation in x…

Q: Find the derivatives of: d/dx (ex-e-x/ex-e-x) And the derivatives of: f(x)=ln((2x+1)3/(3x-1)4)

A: the given expressions is: dex-e-xex-e-xdx the given function is: f(x)=ln2x+133x-14

Q: 5. а) Find the derivative of y = (cosh r)*. Show that the function y = e -2" (sin 3x + cos 3.x)…

A: we have to find the derivative of the function y=(cosh x)x2

Q: 6. Find the derivative of function. a) y = (x - 1)ā + 2x2-4x+7 b) y = cos* 3x * arcsin 3x2 |3D 3 c)…

A:

Q: 1) Find the derivative of y with reference to < Y 블+름 2y Y

A: Here is the solution:

Q: Find tte implicit derivatives of the (x-y)3 = (x+y)2

A:

Q: 24. What does it mean to say that dV is an exact differential?

A: What do you mean by dV is an exact differential.

Q: Solve the problem and give a detailed solution. Find the 3rd derivative of y = ln(cos(e3x))

A: Note ÷ I have used chain rule and product rule multiple times. Please look carefully.

Q: equation

A:

Q: Find the Differential Equation of (sin2x-2ycosx)dx=2dy

A: First we compare given differential equation with dy/dx+Py=Q and find integration factor using…

Q: Find  dy dx  by implicit differentiation. x2y3 − 12xy2 = 4

A: The given expression is, x2y3-12xy2=4 Differentiate on both sides with respect to x of the…

Q: Find the first derivatives of y = cos x tanx

A: Given: y=4cos x+1tan x

Q: Find a function of the differential equation: y' = x3-2 sin x

A: topic - differential equations

Q: Given the differential equation: D´(sin x- cos x+ 3e* +x²) What is the fourth derivative? a - sin…

A:

Q: Solve the differential equation tan x- dy ey-cotx dx

A:

Q: 2 a) FIND BY IMPLICIT DIFFERENTIATION: x*y³ = -8 %3D dx b) EVALUATE THE DERIVATIVE FROM PART a AT…

A: Given: x4y3=-8

Q: Find dy/dx for the equation x3y2=2 using implicit differentiation.

A: Given,            x3y2=2

Q: The population of fish in a lake grows logistically according to the differential equation where t…

A: Logistic growth model of fish is given by dydt=0.1y1-y2500                      (1) Initially lake…

Q: can you help me step by step with this problem?

A: Let z= 6x^2+1 Substitute that. Then take d/dx on both sides.

Q: 1. Find by implicit differentiation for xe = 2xy + y³.

A:

Q: a) Find dx using implicit differentiation: x + y² = 2xy³ + 1 b) Find the equation of the tangent…

A:

Q: Solve for the differential of y when y- sinax. x= and dx O o o

A:

Q: dy dz a ) e-π7z In(y) = x²z

A: Detailed solution is given below.

Q: Convert y'=Xy ʻ-y into an exact differential equation.

A: