The particular solution y, of the differential equation y" + 4y' + 4y = 3x? + 1 is (1/8) (1-2x+6x^2) O None of them O (1/8) (11-12x+6x^2 ) O (1/8) (11-15x+6x^3 )

Q: Find the general solution of the given ODE x +1 y': y* +1 x? + r- - y? = x +4x + k Option 1 O Option…

A: integration

Q: Find the derivative of f(x)= x% (x% + x% +x%

A: Find the derivative

Q: 2. A bushfire spreads with burning area according to the following function, A(t) = 160t – 40t2 (in…

A: Let's find.

Q: Which of the system of equation has no solution? 2х - 4y%3D 4 – 3x + 6y = – 9 а. С. X— 2у %3D 3 | 3x…

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Q: Find the angle of the largest right circular cone which can be inscribed in a sphere of radius 9…

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Q: The volume of the solid region, in the first octant, that lies below below the surface, z = above…

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Q: 0 14 (x² + 4y) dæ dy 4

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Q: Solve the equation (2xy - tan y)dx + (x^2 - x (sec y)^2))dy = 0

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Q: The technique used to prove that x4 x3 - 5x + 5V5 tan¬1 3 x² + 5 dx + C - - is Long (Euclidean)…

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Q: For the number 70260.011000 What is the number of significant digits and what are the significant…

A: Number of  Significant digits = 11

Q: Q3: Find gradient of the following function at given point 1) f(x, y) = y –x, (2,1) 2) g(x, y) = y –…

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Q: Find the slope of the tangent line to polar curve r = 7 cos 0 at the point

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Q: x²dy + (y? txy) dx 3-

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Q: Ql: If f(s,t) = s²t+ In(t² – s) find the value of a) atas Q2: For the following function prove that…

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Q: Consider the differential equation (x- 1)y" + y' = 0. By using power series so- lution about the…

A: Please see the below picture for detailed solution.

Q: Differentiate Зх — 6 y = csc 5x2 + 9 A. Зх — 6 Зх — 6 - y' = cot csc 5x2 + 9 5x² + 9 ) В. Зх — 6 Зх…

A: Differentiation

Q: Find the general solution of the given ODE: dy _ x²y – 4y dx x + 2 (x² y = Ce2 = ce) (x² = Ce2…

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Q: 1. Find the smallest distance from the point (0, c, 0) to the surface y = x² + z².

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Q: Given y, (x) = x² is solution for the differential equation x?y" – 3xy' + 4y = 0 Using the reduction…

A: We have to find the solution of the differential equation.

Q: 2) z= (1+t²)(3 - 2y); z' Ans: z' = -2(3t? + 3t + 1)

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Q: 2x3 = (3xy + 1)2 Implicit Derivative with Solution and Answer

A: Given : 2x3=(3xy+1)2   To Find : Implicit derivative

Q: Using the method of undetermined coefficients, a particular solution of the differential equation…

A: Given differential equation is y''-16y=2e4x. The characteristic equation is m2-16=0⇒m=±4. So, by the…

Q: For some constant a, the following improper integral a | (x2 + 1)e2×dx 2х converges to converges to…

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Q: €) In VEx dx d) so sce x e Serx tumx dx

A: The objective of the question is evaluate the definite and indefinite integral.

Q: A kite is flying at a constant height from the ground at a speed of 2m/s. If the kite maintains the…

A: Draw a schematic diagram of given figure.

Q: Graph the function. Use the graph to find the indicated limit, if it exists. x20 lim f(x), fx) = -…

A: solution:-f(x)=x3 ,         x≥0-6x  ,    x<0left hand limitlimx→0-f(x)=limx→0--6x=0right hand…

Q: Mathematics

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Q: } Consider the initial-value Question 2 ( problem y" + 4y = 5 sin 3t, y(0) = 0, y(0) = 3. (a) Use…

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Q: To prove that 2 dx 1+ (In x)2 + In x+c = 2 In %3D X1 + (In x)2 we use the substitutions U = Inx then…

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Q: For the following function f(x), find f(0) and f(2). if xs0 x2 f(x) = if 0 <x<2 x+3 if 2sxs4 4-x…

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Q: 4.) f(x) = etinlx)+cos (x) 2+4x+4 5.) (x) = = 6.) S(x) = +r-s)(ar-7) 622-131+7

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Q: log x y = dy dx 5+5ln5logx x² In5 dy 5-5ln5log x dx x² In5 Option 4 Op tion 3 dy _ 5-5ln5logx x² In5…

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Q: The polar equation of the curve is expressed as r = 2sine + 2cose. area bounded by the curve.

A: To find the area.

Q: Find the general solution of the given ODE * (y² – y) dx + x dy = 0. - y=c 5 +4x + k Option 1 Option…

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Q: 3) [- y" + 3y - 4y = 20, | Given the IVP: У(0) %3D 0, у(0) %3D —5. A) Use the Laplace transform to…

A: Solving

Q: Use the properties of the derivative to find the following. r(t) = ti + 5tj + t²k, u(t) = 5ti + tj +…

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Q: Find the absolute maximum/minimum value for f(x)= x² – 4x +1 on the interval [-3, 3]

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Q: Suppose that f (x, y) has continuous second-order partial derivatives everywhere and that the origin…

A: Given a function f(x,y)

Q: f(x) is a functicn given by Icosxl Assume that floe) find the pourier Series for of fe).

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Q: Without evaluating the constants, the partial fraction decomposition for 5x² – 3 f(x) (x³ – 4x²)(x²…

A: We have to solve partial fraction.

Q: re' dy + +1 dr =0 O (y – 1) e + + In z = C 2. O-(y+1) e + Ine =C 2 O (1- y) e + 1. O 2y - e + +In=C

A: To solve given differential equation

Q: If f(x) dr = 6 ,what is the value of f(5 – 1) dr

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Q: did not answer my question

A: Apologies for the inconvenience.   Required formulas: ddxfg=ddxfg+fddxg  Product…

Q: Solve the equation (y - (cos x)^2)dx + (cos x) dy = 0

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Q: 5. (1 + e*/") + e*/ dy

A: Solution

Q: Determine whether F(x, y) = 3xi + 7yj is a conservative vector field. find a potential function for…

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Q: Match each 0 with its corresponding quadrant location. -5 , cos O is negative 1 tan 0= Quadrant IV…

A: To match each θ with its corresponding quadrant location.1 tan θ=-512, cos θ is negative.2 cos…

Q: Given the series E n10 Which one of the following gives lim n=1(-10)+1 Select one: 3 10 1 None of…

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Q: Write z1 and 22 in polar form. 21 = -36, z2 = V3 +i Z1 Z2 Find the product z1z2 and the quotients 2…

A: Let's find.

Q: For the following.problems, you need to provide a clear and detailed solution. Work Problem 1 i- :):…

A: We can solve this as follows: