Find the general solution of the given second-order differential equation. 3y"+y' = 0 y(x) = =

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Q: Solve the given initial value problem. y" - 4y' + 3y = 0; y(0) = -1, The solution is y(t) = y'(0) =…

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Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

A: Solution ) we have option 3rd  y"+ 4y = 0 Auxilliary equation  m2 + 4 = 0 m2 = -4 m = √( -4 )  m =…

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Q: Solve the given differential equation by undetermined coefficients. y" - 2y' - 3y = 12e* - 12 y(x) =

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Q: Find the general solution of the given higher-order differential equation. d'u 분 700분 - 20분 +7. dr5…

A: The given differential equation, d5udr5+7d4udr4-2d3udr3-14d2udr2+dudr+7u=0

Q: 2. The function ƒ(x) = x² − 4 is transformed to g(x) =— (x² − 4). Compare the domain, range,…

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Q: Please solve part d)

A: To determine the points on the curve y=tan-1x, where the slope of the tangent line is the curve…

Q: WHAT IS O H|5 Se-5x dx 1 e -5x + C -e e-5x + C -¹e-5x + C 5 e-5x + C

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Q: Solve the initial value problem by Laplace y" +4y=20 e y(0)=3, y'(0) - 12

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Q: ow many values of a are there such that lim h→0 (sin ¹(a+h)-sin h ~ ²² (a)) = = 4?

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Q: For the given differential equation, what is the a) order, b) degree of the differential equation,…

A: The given differential equation is d3ydx35-7xd2ydx23+5dydx=11ey

Q: Consider the function on the interval (0, 27). f(x) = 1/2/20 + COS X (a) Find the open intervals on…

A: topic- Relative extrema of a function.

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Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

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Q: 1 Find the partial derivatives with respect to x for the function f(x,y) f = O O 9y³ x-y 9y3 (x-y)2…

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Q: Consider the differential equation x²y" - 6xy' +10y = 0; x², x5, (0, ∞). Verify that the given…

A: We need to find general solution.

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Q: Prove the identity. cos(3x) − cos^3 x = − cos x sin^2 x − sin x sin(2x)

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Q: Match the solution curve with one of the differential equations. f Ala Oy"+y=0 y" - 4y' - Sy=0 Oy" +…

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Q: el For the function z = f(x,y) = - 4x³ -6y² - 7xy, find t V ne ON dz dx dz 3x forr || f(-5,4)=…

A: The given function is: z=fx,y=-4x3-6y2-7xy   As we know that; The Power Law: ddxxn=nxn-1

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Q: Write an equation for the function graphed below -7 6 5 4 -3 -2 y= 50 on it'st 72 3 Q

A: Topic = Functions

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A: Given the function, gx=1x-1if x>0x2-1if x≤0

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A: This is a problem of ODE. Please follow the procedure given below.

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Q: Question 28 to determine the instantaneous rate of change of 3, to the nearest tenth.…

A: Explanation of the answer is as follows

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Q: (a) Determine whether the series (b) Determine whether the series ∞ n=1 ∞ n=1 n+1 n³ +3 is…

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Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

A: Given general solution of the equation y=C1e-4x+C2e-2x

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Minimize…

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Q: Find the area between the curves. x = -5, x=2, y = 2x² +5, y = 0 The area between the curves is…

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Q: Determine whether the given set of functions is linearly independent on the interval (-∞, ∞o). f₁(x)…

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Maximize…

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Q: You go to the doctor and he gives you 14 milligrams of radioactive dye. After 12 minutes, 6.5…

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Q: Determine whether the given set of functions is linearly independent on the interval (-∞0,00). f₁(x)…

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Q: -2y -2y (²²7) dx + e dy = 0 ex + x

A: Different ial eq is homogenous.

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Q: integral

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Q: Evaluate the integral of x cos 2x dx with limits form 0 to pi/2. (A) -3/4 B 0.75 C -0.5 D 1/2

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Q: 9 P cost D2 + 1 }; రె 2 cos²x T+a {

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Q: Use sigma notation to write the sum. 4 4 1 + 2 1 + 3 4 1 + 1 + + + ... + 4 1 + 19

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