Find y as a function of t if 64y′′+304y′+361y=0, y(0)=3,y′(0)=9. Y=

Q: Compute the values of dy and Ay for the function y= e4z + 5z given z = 0 and Az = dz = 0.02.

A: Given x = 0, dx = ∆x = 0.02            (1) Here y = f(x) = e4x+5x

Q: Find all the points of g(x, y) = x³ − 3x + 3xy² where a relative extrema might occur.

A:

Q: 4. For the below function, find the stationary point (s) and prove if a maximum, minimum, or saddle…

A:

Q: Does the given equation F(y; x) = x° - 2a²y+ 3xy- 22 0 define an implicit function around the point…

A:

Q: Find fryz from the functions f(x, y, z) = 4x³y² – e²y* ++ 4y – x16 %3D - |

A: To find the third order partial derivative of the function fxyz f(x,y,z)=4x3y2-ezy4+z3x2+4y-x16

Q: Find the linearization L(x,y) of the function f(x,y) = x2 - 4xy + 5 at Po(5,4).

A:

Q: 2²y. 3. Consider the function f(, y) =

A:

Q: 4 - Find the direction A in which the function f(x, y) = x cos y + y sin x decreases most rapidly at…

A: We have to find the direction A in which the given function decreases most rapidly.

Q: The function g(t) = \t| is differentiable at 0. True False

A: Given that g(t)=|t|We can write it as:g(t)=t   , t≥0-t , t<0

Q: 4. Find if y is a function of r defined implicitly by da 2*y + sin a = xe" + In

A:

Q: Find the linear approximation of f(x) = e(a) at a = 1.

A:

Q: Find all points (x, y) on the graph of g(x) = 1/3 x3 - 3/2 x2 + 1 withtangent lines parallel to the…

A: Given: The function gx=x33-3x22+1, To find: All the points x,y on the graph of given function at…

Q: Find y as a function of t if y(0) = 4, y(0) = 1. y(t): = 64y" - 144y + 81y = 0,

A: Given: The characteristics equation is             64m2-144m+81=0⇒m=--144±-1442-4· 64· 812·…

Q: Find fryz from the functions f (x, y, z) = 4x³y² – e²y+ ++ 4y – x16

A:

Q: Find y as a function of t if y" – 10y' + 21y = 0, y(0) = 7, y(1) = 4. y(t) = Remark: The initial…

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Q: dw the functions w= -5x²-3y².x= cost, and y=sint, express as a function of t, both by using the…

A: Use chain rule for derivative

Q: f(x, y, z) = e2* +e3y + e4=

A:

Q: Find the ditterential of the function y = (x + 1(5x - 3). Sx-x-5 dy = (Sx - 3) *?+ 6x-5 (5x- 3)? dy…

A: Use the quotient rule of differentiation ddxuv=vdudx-udvdxv2. Power rule of differentiation…

Q: YouTrylt 2 Find the linear approximation of the function f(x,y) =In(x- 3y) (7,2) at and use it to…

A: Please rate and feel free to ask any query about any part of the question.  Thanks

Q: of For the function f(x.y) = In (x + 6y), find- of and dy

A: It is partial derivative so when we differentiate with respect to one variable consider other…

Q: 4. Find the orthogonal trajectories of the family of curves y=Ce*™ +10

A: We have to find the orthogonal trajectories of the family of curves

Q: Find the vertical trace of the function at x = 1: g(x, y) = cos√x² + y²

A: Definition : Consider a function z=f(x,y) with domain D⊆R2. A vertical trace of the function can be…

Q: Verify that the indicated function y = p(x) is an explicit solution of the given first-order…

A: This question can be solved using the concept of derivatives.

Q: Find fryz from the functions f (x, y, z) = 4x³y² – e²y* + + 4y – x16

A:

Q: Find the differential of the function. z = 7t − 7/t2

A: zt=7t-7t2

Q: Find the equation of the line tangent to fƒ(æ) = e² (x² + 3x) at the point (–2, –2e¯²). O y = -3e-2…

A:

Q: The function f(z) = 1 has a poles at z = %3| ez – 1

A:

Q: 5. Determine whether the functions y, and y2 are linearly dependent on the interval (0,1). Yi = 1+…

A: Linearly independent of the function. Using Wronskian

Q: The x- coordinate of the point on the graph of y = Vx-1 at which the tangent line is perpendicular…

A: slope of tangent of the curve y=x-1 is dydx=12x-1 slope at (x1, y1)dydx=12x1-1=m1if (x1, y1) is the…

Q: Find the linearization L(æ) of the function at a. f(z) = V7, a = -8 L(x)

A: We can find the linearization as below.

Q: 2. Find whether the function F-(* - y' )i + (v² - 3x)j + (:² - xy is irrotational.

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Q: Find the linearization L(X) of the function at a. f(x) = Vx, a = 16 L(x) =

A:

Q: Supposed that z is defined implicitly as a function of x and y by the equation x2 + y2 +z2 = 4. Find…

A: The given data is: x2+y2+z2=4 To find the value of dzdx

Q: Find the equation of the line tangent to y 8xe" at x = 1. O y -8e = 16e(x – 1) O y - 8e = 8e(x – 1)…

A:

Q: A) Find the linearization of the function at the given point. f (x, y) = 1+ y ln (6 – xy), at (5, 1)…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Q.8 Find the gradient Vw ofthe function w = In /x² + y² + z². %3D

A: Given function W=ln(√(x2+y2+z2)) Now we will find the gradient as shown below

Q: Find any value(s) of the constant a such that the line y = ax is tangent to the curve f(x) = -x² +…

A: Tangent of a curved touches the curve only at one point.

Q: Find an equation for the level surface of the function f (x, y) = ln (x² + y²+ z²) that passes…

A:

Q: Find y as a function of t if  y′′+6y′−7y=0, where y(0)=8, y(1)=7   Remark: The initial…

A: See the attachment

Q: 5 B) Find y" for the function y = x + Vx at p(1,3)

A: Given query is to find the double derivative of the expression at point p.

Q: Find the (x, y) co-ordinates of the two stationary points of the function f(x, y) 3x2 + 6xy +2y³ +…

A: Given-  f (x, y)  =  3x² + 6xy + 2y³ + 12x - 24y So,

Q: for the function f(Z) z²-2z find the (z+1)° (2 t4) residues at singular points.

A: The residue of f(z) is solved below

Q: find the linearization L(x, y) of the function ateach point. ƒ(x, y) = 3x - 4y + 5 at a. (0, 0), b.…

A: fx, y=3x-4y+5 Partially differentiating with respect to x, we get fxx, y=31-0+0=3 Partially…

Q: 1. Find the stationary points of the following functions. (a) f(x,y) = x²y+ 2y² – 2xy + 6 - (b)…

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Q: Q3: Find fxx of the function f (x, y, z) = -In/1-x2 - y2 – z2 %3D

A:

Q: 1. Consider the curve F(x, y) = 0. Show that if F has continuous second derivatives, then a formula…

A: Consider the curve F(x, y)=0. The objective is to show that if F has continuous second derivatives,…

Q: 5. Find y' at the point (0, e) where xy² + In(x² + y) = 1.

A: Find y' = dy/dx At point (0, e)

Q: Find the G.S. about xo = 0 for: (x² + 4)y" + xy = x + 2

A:

Q: Consider the curve in the xy-plane represented by the two equations below. The slope of the line…

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Q: Find y as a function of t if y(t) y" + 2y + 10y = 0, y(0) = 8, y'(0) = 9.

A: The given DE is: y''+2y'+10y=0 The auxiliary equation of the given DE is:…

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.