9. Find a quadratic function y = ao + a1x + a2x² satisfying y(1) = 1, y(-1) = 2, and y'(1) = 2.

Q: y', In(y) 1 y(e) = 1. x² In(x)

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Q: The differential equation obtained by eliminating the arbitrary constants A and B from the relation…

A: y=Ae5x+Be6x

Q: 2. xyy' = 1+ y? when x = 2, y = 3

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Q: b) Use the initial condition y(0)= 2.14 to find the particular solution of dy -2y + x2 + 2x = 0 dx…

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Q: Find the differential dy of the given function.     y = 3x2/3

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Q: 10.Obtain the general solution of y(8x – 9y)dx + 2x(x – 3y)dy = 0

A: First we find tha integrating factor of given differential eq then we get exact differential eq.So,…

Q: 1. Find the differential dy in y= 2x4-3x3-5x 2. Use differentials to find approximate values for…

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Q: Solve the initial value problem for an arbitrary f(t) function. y"+4y'+4y=f(t),  y(0)=2 ,  y'(0) =…

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Q: What is the differential equation of the orthogonal trajectories of the family of curves x2 - 3xy-…

A: Given family of Curve is x2-3xy-2y2=C

Q: 2. xyy' = 1+ y? ; when x = 2, y = 3

A: Given xyy' = 1+y2 and  x=2 >>> y=3

Q: What is the differential equation of the orthogonal trajectories of х3 — Зху — у3 — с? (1) (x +…

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Q: Find the differential of the given functions: 1. y = 3x4 - 5x³ + x - 4 2. u = /2y – y3

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Q: A firm has the Cobb-Douglas production function y = 10x}^^x!7²x}^. Currently, it is using the input…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: b) Use the initial condition x(0) = 2 to find the particular solution of dx - 2x = 2e3t dt

A: We have to solve the given initial value problem  As per the answering guidelines we need to answer…

Q: What is the differential equation of the orthogonal trajectories of x3 = Cy? (1) Зxdx + 2уdy — 0 (2)…

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Q: Solve the IVP u® +u"=e*-2tx with y(0)=1, y'(0)=0, y"(0)=1 (where t is a real constant)

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Q: 3. Find the particular solution of the differen- tial equation: (x² +y² )dy=xydx, given that x=1…

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Q: Solve the initial value problem for y as a function of x. x2 - 16 dy = X, x > 4, y(8) = 0 dx

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Q: Solve the initial value problems for y as a functionof x. (x2 + 4) dy/dx = 3, y(2) = 0

A: Given Data : Differential Equation x2+4dydx=3, y2=0                      1 The given initial value…

Q: Obtain the differential equation of all straight lines at a fixed distance p from the origin * O…

A: The general form of equation of a line which is at a constant distance c from the origin is…

Q: 2. Give the general solution of xy'dy = (x³ +y³)dx in explicit form.

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Q: a) Find a function y whose graph passes through the point (1, -) and satisfies x²y' = y. b) Solve…

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Q: Choose the solution value of x'' + w2x = fsinwt with initial conditions x(0) = 0 and x'(0) = 0

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Q: Show that the function y =  A e-x    + B x e-x satisfies the differentialequation y"   +2y' + y  =0

A: The given differential equation is y''+2y'+y=0. Let y=Ae-x+Bxe-x. This implies that,…

Q: find a particular solution yp of the given equation. primes denote derivatives with respect to x.…

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Q: 1. e-st cosh t dt 2x +4 2. 2x2 + 21x + 34

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Q: 2. If y is the solution of the initial value problem = 3(y - 1)(y-2) with y(1) = 3, what is lim…

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Q: Find the particular solution of the nonhomogeneous ODE. y"-4y' + 3y = x² + e* + sin2x

A: We will find out the required particular solution.

Q: (x² + 4) dy 山 3. y(2) = 0

A: we know that ∫dxx2+a2=1atan-1xa+C,  where a>0 see below the answer and calculation

Q: solve the Initial Value Problem using Separation of Variables. y' = xy2, y(1) = 2

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Q: What is the differential equation of the orthogonal trajectories of the family of curves x2 - 3xy-…

A:

Q: (d) The GoldPlus Company determines that the marginal cost for their Aiibe 64GB flash drive is given…

A: Given that : Marginal Cost Function is : dCdx=-0.02x+6. We can achieve Total cost function by…

Q: 5. z = yex+x Iny xey-y lnx

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Q: - Show that the partial differential equation = 0 has the general solution u(x, y) = e"[f(x) + g(y)]…

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Q: 2. Show that the substitution z=y(1-n) will reduce the Bernoulli Equation y' + f(x)y = Q(x)yn to a…

A: The solution is given as

Q: Express the solution of the initial value problem dy 2x- dx as an integral = y + 2x cos x, y(1)= 0

A: Simplify and convert in linear equation.

Q: Verify that u(r, t) = f(e-"x) solves the initial value problem (au + z8,u = 0, u(x,0) = f(z).

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Q: Solve the homogenous diff equation of; xdx . (y+1) dy y³ e-x = 0

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Q: 23 3. Determine whether the function y(x) = 2sin4x is a solution to the initial value problem of y"…

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Q: Find the differential equation of the quartics : c^2y^2 = x ( x - a )^3 with c held as fixed.

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Q: Solve the initial value problems for x as a functionof t. (t2 + 2t) dx/dt = 2x + 2 (t, x > 0),…

A: t2+2tdxdt=2x+2⇒dx2x+2=dtt2+2t Now integrating on both sides, we get…

Q: 1. Eliminate the arbitrary constants on the given equation: y = A + Be*

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Solve the initial value problems for y as a functionof x. (x2 + 1)2 dy/dx = √x2 + 1, y(0) = 1

A: x2+12dydx=x2+1⇒dydx=x2+1x2+12⇒dydx=1x2+132⇒dy=1x2+132 dx Now integrating on both sides, we get…

Q: Find the solution to the initial value problem as an explicit function of the independent variable.…

A: Given : (t2+1)y'+y2+1=0,   y(3)=2

Q: 3 9 dx dt -1 -3 with x(0) 4 Give your solution in real form. X1 = X2 = ||

A:

Q: Solve the initial-value problem for yy as a function of xx. (64−x2)dydx=1,y(0)=5(64-x2)dydx=1,y(0)=5

A: (64-x2)dydx=1⇒dy=dx64-x2integrating,                ∫dy=∫dx64-x2+c      [c=…

Q: 2. Give the general solution of xy dy = (x³ + y³)dx in explicit form.

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Q: 7.Obtain the particular solution of (1 – xy)-2dx + [y? + x²(1 – xy)-²]dy = 0 when x = 2, y = 1

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Q: What is the differential equation of the orthogonal trajectories of the family of curves X2 -…

A: