(x, y) = (0,0) %3| = {r3+y3' 0, (b) f (x, y) (x, y) # (0,0)

Q: an integrating factor for the DE dy+ydx=e3x dx is  1)ex 2)x2 3)y 4)x 5)ey

A: To find an integrating factor for the DE dy+ydx=e3x dx

Q: 2 y

A: According our guidelines i solve only first question.For second solution please resubmit again…

Q: The integrating factor of + 2.xy= 5x² is dx dy а. b. x2 e 2 C. 1 d. et

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Q: Reducible to Homogenous method dy X-y-3 x-y-1 dx

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Q: dy 2х + ху is separable. dx y2 + 1

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Q: dx dy (a) dt di -y = 6e3t, 2 dt -3x +-3y = 6e3t; dt x(0) = 3, y(0) = 0.

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: (dx — Зх — 2у dt dy 3D —х + 3у — 2z dt dz = -y + 3z dt %D (λ1, λ = 3, λ5)

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Q: ∫ 2y dx + 3x dy   where d is described by 0 ≤ x ≤ 1, 0 ≤ y ≤ 1

A: Consider the given integral is, ∫2ydx+3xdy The above equation is of the form M=2y and N=3x. Then, by…

Q: Find both first partial derivatives. h(x, y) = e-(x9 + y9) h,(x, y) = h,(x, v) =

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Q: dx dy -- x - 2y = 16te', 2x – dt - 2y = 0, x(0) = 4, y(0) = 0 dt

A: We will find out the required solution

Q: The integrating factor of the DE   y(2x - y + 1) dx + x(3x - 4y + 3) dy = 0 is

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Q: I-x² f (x, y, 2) dz dy dx 1-x² Jo

A: we have to find the region of integration

Q: ý =y+X ans y= as +aoX+(a+). %3D a. %3D e +e-X-1

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Q: COS f(2, Y) af af dy f(x, y) = log, (3x) af %3D fe dy

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Q: 2. [f 5y ey dA, F- {(x, y): 0 s x s y?, 0 s ys 2} F

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Q: What is the integrating factor of y (x² + y) dx + x (x2 - 2y) dy = 0? -1

A: We will find out the required integrating factor.

Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = sec-1 (x + yz)

A: Given that f(x, y, z)=sec-1(x+yz)

Q: b. y = cosh(arctan 3x) C. y = 4a/ cosh a d²y d. for x = 4v2t2 + a, y = a² – t² dx2 %3| -

A: Given functions are  b) y=cosh(arctan3x) c) y=4acosha d) d2ydx2 for x=42t2+a , y=a2-t2

Q: 3. (4r'y-15r-y)dt + (r +3y-1)dy = 0 CS Scanned with CamScarner

A: We can solve this using exact equation of differential equation

Q: d³y dt3 dy + 4 dt2 + 5 dt + 2y = 10 cost y(0) = 0, y'(0) = 0, y"(0) = 0 %3D

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Q: 2e | 3జy S S dy da = Vsin(zy)

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Q: +[2yln [2yin (3 3y²dx 3siny dy = 0 ;when x = 1, y = 0 5x x2+3x x+3,

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Q: An integrating factor of (x³y² + x)dy + (x²y³ – y)dx = 0 is (a)수 (b) (c) (d)을 2xy 2x

A: Given differential equation is x3y2+xdy+x2y3-ydx=0

Q: X ( CSC ( X ) - Y Inx- X y - y dx + x dy = 0 dy - (Iny - Xdx X

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Q: 3D In Vi dt y = x/2

A: First of all we will evaluate  ∫lntdt=∫ln(t)12dt=12∫ln(t)dt=12ln(t)∫dt-∫ddx(ln(t))∫1dtdt(used…

Q: The linearization of ex at x = 0 Derive the linear approximation ex = 1 + x at x = 0.

A: Given, ex ,x=0 We know that, The formula for the linearization is, Lx=fa+x-af'a

Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = ln (x + 2y + 3z)

A: Given, ƒ(x, y, z) = ln (x + 2y + 3z)

Q: Evaluate //| (x + y – 2z) dV where E = {(x, y, z) | - 2 < y < 0,0 < x < y, 0 < z < x + y²}

A: A detailed solution is given below.

Q: y' + 4y = e^(4t) %3D

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Q: Find the first partial derivative of the function 11. If F(x, y) = e* tan(x + y), find F, (0, T) and…

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Q: dx = -y+y(x² + y² dt dy = x – x(x² + y²) - dt

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Q: dy = (x – 2)e-2y dx einitial condition y(2) = In(2).

A: Explanation and solution is given below.....

Q: x² + y² = (2x² + 2y² – x)', (0,¿), (cardioid) -

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Q: Solve simultaneous equation dx/dt=2x+3y , dy/dt=x+4y , x=-3 , y=1

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Q: Find both first partial derivatives. h(x, y) = e-(x° + y9) h,(x, y) = %3D h,(x, y) = %3|

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Q: ution of yl = x+xy2 W

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Q: (3z²+5z+3)dz (z- 2)(z+3) Integrate:

A: The given integral is ∫(3x2+5x+3)(x-2)(x+3)2dx

Q: d²x dx + 4 + 5x – 10 = 0, when t dt 0, x = 0, x = 0 %3| %| dt2

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Q: 5. Find the second partial derivatives of f(x, y) = x²y³ + 3y?

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Q: dy dy + 7 dt + 10y = e-t dt2

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Q: d²x dx + 4- + 5x – 10 = 0, when t = 0, x = 0,x = 0 dt2 dt

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Q: Find the integrating factor of : 2y(x2 - y+ x )dx + (x² – 2y)dy = 0 ху O y 2х e2x

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Q: a) Find the differential dy of y=x2+2x+5. (b) Evaluate dy for x=3, dx=1/2. (a) dy=????????? dx (b)…

A: GIVEN THAT y=x2+2x+5

Q: ди + 3x- = 1 + u, dx ди -co 0, dt u(x, 0) = f(x).

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Q: *= 1+?-,y = -x²,x > 0 2. = x³(y – x)² +2, y1 = x,x > o у 1. %D = x³ (y – x)2 + dx , Υ1 - x, x > 0 dy…

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Q: y∅=y^-2 is the integrating factor of 2y(x+y+2)dx+y^2-x^2-4x-1)dy=0

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.