Determine whether y is a function of x                                                             x2y − x2 + 4y = 0

Q: Find y as a function of x if y′′′+81y′=0, y(0)=0, y′(0)=−81, y′′(0)=−81. y(x)=

A: Given that,                    y''' + 81y'=0.......equation(1)                 y(0) =0,  y'(0) =-81,…

Q: Find y as a function of x if x*y" + 11xy + 25y = x', y(1) = -4, y(1) = 0. y =

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Q: Find the image of the function f(x.y) = 36 + 1\4 v(9x² + 4y³)

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Q: Find y as a function of x if x'y" + 5xy' + 4y = 0, y(1) = 9, y'(1) = -2. y =

A: Solution :-

Q: Determine whether z is a function of x and y. xz2 + 2xy − y2 = 4

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Q: If possible, represent y as a differentiable function of x.                                    a. x2…

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Q: Find a function y(x) such that 5yy' = x and y(5) = 8. y =

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Q: Find a function y(x) such that 8yy' = x and y(8) = 5. y = ||

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Q: Graph and shade the domain of f(x, y) = vy + x² – 2.

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Q: Find y as a function of x if y′′′−14y′′+48y′=0, y(0)=1,  y′(0)=8,  y′′(0)=4. y(x)=

A: The given differential equation is  y′′′−14y′′+48y′=0, Boundary conditions are y(0)=1, y′(0)=8,…

Q: Find y as a function of t if 324y′′+684y′+361y=0, y(0)=9,y′(0)=9.

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Q: Find yy as a function of xx if y′′′−8y′′−y′+8y=0 y(0)=4,  y′(0)=−6,  y′′(0)=130.

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Q: Differentiate the function. z(y) = A/y12+Bey

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Q: * Find y as a function of æ if y" – 8y" – y' + 8y = 0, y(0) = 4, y'(0) = -6, y" (0) = 130. y(x) =

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Q: Find the function satisfying y' x + 3 and y(0) = 2 ... 2y + 5

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Q: Find yy as a function of x if y′′′−7y′′+12y′=6e^x y(0)=30,  y′(0)=19,  y′′(0)=12

A: y′′′−7y′′+12y′=6ex        y(0)=30,  y′(0)=19,  y′′(0)=12 given differential equations is linear…

Q: Find y as a function of x if x^2*y′′+2xy′−20y=0 y(1)=−6,  y′(1)=1.

A: Find y as a function of x if x^2y′′+2xy′−20y=0 y(1)=−6,  y′(1)=1.

Q: Determine whether y is a function of x…

A: For a function to be a function of x, the two variables say y and x must be separable…

Q: Find y as a function of x if x²y" – 3xy' + 4y = x", y(1) = 3, y'(1) = –5. y =

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Q: (: Find y as a function of x if y" + 64y' = 0, y(0) = -1, y'(0) = -24, y"(0) = 0. y(x) =

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Q: Draw the domain of the function: f (x, y) = Vx² + 9y² – 36

A: Please refer the attached image for complete solution. THANKYOU.

Q: Find y=f(x) if f''(x)=4x^2, f'(0)=3, and f(0)=2.

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Q: Find y as a function of x if x²y" – 3xy – 12y = x², y(1) = -7, y(1) = -7. y =

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Q: Consider the function f(x,y) = x² + xy – 5x – y+ 1. Then:

A: Consider the given function as fx,y=x2+xy-5x-y+1

Q: For function f (x, y) = x2+1

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Q: Differentiate the function. y= (2x-5) (1-x*)1 dy %3D xp %3D

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

Q: y" – 12y" + 32y = 42e",

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Q: Find y as a function of a if y(0) = 2, y(0) = 3, "(0) = 7. y(x) = y"9y" + 18y = 0,

A: y'''-9y''+18y'=0y(0)=2, y'(0)=3, y''(0)=7To Find: y(x)

Q: Find a function y(x) such that 2yy' and y(2) = 5. y(x) :

A: Given that 2yy'=x   and  y2=5. Solve the above equation as follows.…

Q: Find a function y(x) such that 3yy' = x and y(3) = 3. y =

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Q: Find y as a function of x if y′′′+25y′=0, y(0)=6,  y′(0)=35,  y′′(0)=−100. y(x)=

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Q: Determine whether z is a function of x and y + z2 = 1

A: see below the answer and explanation

Q: Consider the function of two variables F(x, y) = − 2 x² – xy – 2y². ´+z+y.

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Q: Identify the equation that defines y as a function of x (a) x+(y-1)² = 3 (b) x2-y 3xy (c) 3x+5y = 1…

A: (a) x + (y-1)^2 =3       this equation gives two value x (b) x2 - y2=3xy    it also give two values…

Q: Let f : Z4 → N be the floor function f(x) = [(x – 1)/2].

A: Given f:ℤ+→ℕ be the floor function defined by  fx=x-12 For x=1,  fx=02=0<1 For x=2 fx=12=0<2

Q: Find the function y(x) such that y′′(x) = 0 with y(1) = 2 and y′(1) =−1.

A: Given y′′(x) = 0 with y(1) = 2 and y′(1) =−1. y''(x)=0, with y(1)=2 and y'(1)=-1Now integrate both…

Q: Find y as a function of a if y(0) = 7, y'(0) = 10, "(0) = 36, "(0) = 0. y(x) = 0 y(4) 12y" +36y" =…

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Q: Find a function y(x) such that 6yy' = x and y(6) = 3. y =

A: The objective of the question is solving the differential equation.

Q: 2 Ax.y)3+ V 3x + 3y

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Q: Consider the function f (x, y)=-2x'+3x'y+2 y°-9y+5

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Q: Find y as a function of x if y′′′+49y′=0, y(0)=8,  y′(0)=49,  y′′(0)=98.

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Q: Find y as a function of a if y(0) = 8, y(0) = 4, y"(0) = 134. y(x) = y"8y" -y + 8y = 0,

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Q: Find a function y(x) such that y'(x) = x² In(x³) – (x² + 1)¯ and y(1) = 2.

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Q: Consider the function f(x, y) = x²y+ y8 – 75y.

A: In this question, we find the critical points and check for local maxima and minima.

Q: Find all functions f: R → R for which f(x + y) – 2f(x – y) + f(x) – 2f(y) = y – 2 |

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Q: For the function f (x, y) = /(x – 1)2 + y2 + 1

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Q: Find all functions f : R → R for which f(x + y) − 2f(x − y) + f(x) − 2f(y) = y − 2

A: We are given that f:ℝ→ℝ, which follows: fx+y-2fx-y+fx-2fy=y-2 for all x,y∈ℝ.

Q: Find y as a function of æ if z²y" – 4ry' – 36y = 0, |у(1) — 6, у(1) — -6.

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Q: Determine whether z is a function of x and y. x2z + 3y2 − xy = 10

A: Given expression:                                      x2z+3y2-xy=10   Taking half of the terms to…

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.