ƏM Consider the equation (y² – 2x)dx + (2xy+ 1)dy = 0. If f (x, y) : ƏN what is the value of əx' ду f(1,2)? A -1 2 1

Q: Calculate the second order differential of the function f(x,y) = x^{4}*y^{2}+2*x-y^{7}+3 Attached…

A:

Q: general equation of (z-t)dz=(z+t)dt

A:

Q: The temperature in degrees Celsius on the surface of a metal plate is given by T(x, y), where x and…

A:

Q: 4. Determine the directional derivative of f(r, y, z) = xe"+rsinz+a²y at the point (2,0, ) in the…

A:

Q: The order and degree of the differential d³y V dy equation: 7+ i. - dx3 dx 3, 2 7,3, 3, 1 3, 7

A: The order of a differential equation is the highest order of the derivative that is present in that…

Q: Find the direction in which f (x, y, z) = z exy increases most rapidly at the point (0, 1, 2). What…

A: We have given f(x, y, z) = zexy and the point (0, 1, 2).

Q: tan-1 y y² +1 tan-1 y ) dy

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

Q: a) Find the directional derivative of f(x, y, z) = x²yz + 4xz² at (1, -2, 1) in the direction 2i - j…

A:

Q: p) What is the directional derivative of /(x,y,z)=(x+2y+3z)* at point (1,-1,1) in the direction of…

A:

Q: Evaluute the integra dx 0 16+49x2

A: Here we have to evaluate I=∫-∞∞dx16+4x2

Q: dy =-2x tan y, 1- y(0) = 1/2. dx 2- 2 ydx CSOS 3- e*dx-ydy 0, y(0) = 1

A:

Q: Tangent to the curve z2 = 2xy + x2 , z = 3 , at the point ( 1, 4, 3) %3|

A: For a surface of the form: f(x, y, z)=0, the equation of the tangent at x0, y0, z0 is defined as…

Q: siny µ(x,y) = ye* is an integrating factor of dy 3D0 2e sinxldx cOsy+2e COSX Select one: True False

A:

Q: Can i get help step by step please

A: Find the product rule of derivation and find dy/dx,

Q: Compute dy/dx in terms of x and y. 20. Thermodynamics texts use the relationship az %3D ax az…

A:

Q: Using figualve mme thod X + 2 dt 2. dy X - 29

A: To find the eigenvalues λ of the matrix A, solve the characteristic equation A-λI=0 for λ. To obtain…

Q: Solve ux – uy +yu = 0, where u is a function of x and y. %3D

A: Given: ux-uy+yu=0. The objective is to solve u, where u is a function of x and y.

Q: dz/dx&dz/dx at the point (1,1,1) Find the value of if the equationxy + z³x - 2yz = 0.

A:

Q: e'sin" ) *sin sech (x-2) * sech (x-2) F (x) = Explain why g(z) - 0, is not differentialble at a2. if…

A: Here, fx=exsin3πxx2sechx-23

Q: lim (z,y) (1,1) 2x – ry – y 22 – y?

A:

Q: Siny dy = Cas y (l-x Cosy) Cauy) %3D

A:

Q: Consider the function f(x.y) = 2 –-y, whose graph is a paraboloid (see figure). a. Find the value of…

A: fx,y=2-x23-y2Point 0,3Unit vector U^=-22,-22

Q: sin³ y dy 2. S 1- siny

A: Solution Given   ∫sin3y1-sinydywe need to find the integral

Q: Can i get help step by step please

A:

Q: dy when t = 0: dx Find

A: dydx = ? at t=0.(a)Given equations - y = 2t-4-3               ..................(1)x = 3e-2t…

Q: exact diffential equation of (y+2xy³)dx+(1+3x²y²+x)dy=0

A: We have to solve the exact differential equation: y+2xy3dx+1+3x2y2+xdy=0 Rewriting the equation, we…

Q: ly Exercise: Find dx 1. y. 10x+3 Cosx y lox +3 Cosx +子 Cotx 3) 14 Cotx

A: As per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly repost other…

Q: Jx cos 3x dx Using Integration by parts, what should be the u and the dv? O u = xdx, dy = cos 3x Ou=…

A: Given : ∫xcos3xdx    To Find : Value of u and v in integration by-parts

Q: (c) curve y = 5-x", line y=x+3 (d) y= sinx, y=cosx, x= 7 /4, x=7/2

A: Double integers

Q: ue of J. Note that the lows

A: Given ∇.V=1r2∂∂rr2vr+1rsinθ∂θ∂∂θsinθvθ+1rsinθ∂vϕ∂ϕ

Q: dy - 4 - 5y = dy -3t sin(4t) ; y (0) = 3, y (0) = 10 dt2

A:

Q: Cos y dy 1-siny

A: The given integral is: I=∫cos2y1-sinydy   As we know that; The trigonometric identity: sin2x+cos2x=1…

Q: 0Y Find the direction derivative of fcxy)=xy at the paint (2,1), by the dirction of v- i-j

A:

Q: Fx to find dy Assuming - 7x - 9y2 - 2xy = 0 defines y as a differentiable function of x, use the…

A: To find the derivative using the theorem

Q: 3. Consider the function f(r, y) = 'y - 4y at the point P(2,-1). (a) Find the directional derivative…

A:

Q: Use a linear approximation to estimate the change in f(x,y, z) = e2" cos(5yz) when moving from the…

A:

Q: a) If W = F(x ,y),where x =v²-g and y 2vg calculate W +W, %3D b) What is the directional derivative…

A: W=f(x,y) and x= v2-g2 & y=2vg   Wx = dW/dx = (df/dx*dx/dv) + (df/dx*dx/dg) ..............From…

Q: dy BY IMPLICIT DIFFERENTIATION: 9x dx 1. FIND %3D secy

A: We have to find dydx by implicit differentiation: 9x=sec y We know the formula of differentiation,…

Q: = (u² - cos v, u + sint, cos v) x(u, v):

A:

Q: Find the differential of f(x, y) = 3+y² at the point (2, 3). df: ((3x^2)dx+(2y)dy)/(2sqrt(x^3+y^2))…

A:

Q: dy dx 118 (x = 3x - 5

A: Topic:- differential equations

Q: (sinx+1) (cosx+1) dy evaluate dx -If: y =

A: Use the concept for derivative of the form  y = f(x)/g(x)

Q: Use Leibniz's rule to find 히증 11 Textbook dx for y= 0 S 7x² 8t - dt. 8t+1 Ask my instructor

A:

Q: Tangent to the curve z2 = 2xy + x² , z = 3 , at the point ( 1, 4 , 3

A:

Q: z=f(x, y) = 2x +3 y at the point (2, 2, 20) (ii) Use a linear approximation to estima

A:

Q: 2. Prove the formula of the derivative of y = cosec-f(x). d²y and dx2 of the parametric equation…

A: 2. Given y=cosec-1f(x) we need to find the derivative. cosec y =f(x)   (1). But we already know the…

Q: af The maximum rate of change at a point on a function f(x, y, z) is |3D да ylgn ihi

A:

Q: Using Separation Variable. 1.) dy/dx = (2-y)^2 / 2(1+x)^1/2

A:

Q: (D³ + 3D2 + 3D + 2)y = 0

A: Find out the solution.

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.