If f(x) = x³ and g(x) = x + 4, then g(f(x)) is equal to ... %3D %3D O (x+ 4)3 x + 4 O x'(x+4 x +43

Q: Apply Duhamel’s principle to write an integral formula for the solution of  initial value problem…

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Q: x2+x-2 dx If S dx can be resolved into A f+B S f(x)dx + D § g(x)dx , then (x2–1)(2x-x²) Lif(x)dx –…

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Q: b. Find x from the following equation. log 42x = log,27*-1 7x-3 c. Express x+2x2-3x in the form of…

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Q: In(x²+x)-Inx-elnx dx In(e(x+1)

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Q: 1- 24-x = e/2 x3 dy 2- (2xe + e*)dx + (x2 + 1)e'dy = 0

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Q: Find y': y = ez² + 3x² + e²e Oy = e + 3x ln x + e²ex Oy' = e + 3x²-1 Oy = e + 3x² In a Oy = e +…

A: Given y=e12x+3xe+e2e Given query is to find the derivative y'

Q: (x – 2)dx + 4(x +y – 1)dy = 0

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Q: Find the explicit solution of the initial value problem, X +y = x² ln(x) y² where y(1) = 2 and x >…

A: The equation of the form dydx+P(x)y=Q(x)yn is Bernoulli's equation. The equation is converted into…

Q: Consider the following initial-value problem. f'(x) = 6x2 - 4x, F(1) = 3 Integrate the function…

A: *concept:- integration to be perform.

Q: Solve the Initial value problem x' -x=8(t-2),x(0) =x' (0) =0

A: We use the Laplace transform to solve the given initial value problem.

Q: In Bernoulli equation y' - xy = xy³, the value of 1(x) is ex²

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Q: (1) f(x+4)² dx (3) ſ. x² dx x² - 4 (2) √ x²(x³ + 1)² dx (4) √x²0 x² cos 3x dx

A: The given integrals are;  1) (x+4)2 2)x2(x3+7)7 3)x2/(x2-4). Repost the 4th question.

Q: 1-3х 4. y2x – 32 dx V2x – 3x²

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Q: Eliminate the arbitrary constant. xcos(xy) + e^x  lny = c

A: We can use application of derivative in order to solve the given problem.

Q: Find the general solution of : (x² - y² )dx + 2xydy = 0

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Q: Find the general solution of y" – 3y' + 2y 1+e-x°

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Q: 4. Given that Sf(x) dx = 5 and S g(x) dx = -2, find Lr«) + g(x)] dx a. b. $2f(x) dx – ſ, g(x) dx c.…

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Q: 3- Find the Gamma and Beta Function Below : A: 2x°e*dx B: , V2x. (1- x)(1 – x)dx

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Q: Find the general solution of F′(x) = 1/x2, x > 0 and find the particular solution that satisfies…

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Q: (x³ + x²y + x²)dx + (x³ – x²y – x²)dy = 0

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Q: The value C for the solution of the initial value problem f'(x) = x² – 6x + 2, given that f(0) = 0.…

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Q: Find an implicit and an explicit solution of the given initial-value problem. (Use x for x(t).) dx =…

A: The given initial-value problem,dxdt=4x2+1, xπ4=1

Q: Apply Duhamel’s principle to write an integral formula for the solution of  initial value problem…

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Q: #2 du = Ixlux dx 3 13 x 3 dx dv=lnx dx V= x/nx-x Distribute clnx-x). = (1+x) (x I^x-x) -…

A: Using Integration By-parts formula

Q: The value C for the solution of the initial value problem f'(x) = x² – 6x + 2, given that f(0) = 0.…

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Q: Apply Duhamel’s principle to write an integral formula for the solution of  initial value problem…

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Q: x2+3 hence evaluate S x2 +3 7. Express in partial fractions x(x2 +1)' dx, leaving your answer in…

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Q: 2 -e dy=x(xdy-ydx).

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Q: d S[e-In(2t+1)]dr. find g(x) - dx A e-In(2x+1) 2 B (2x + 1)² (2x + 1)² (2x+1)² If g(x) = D

A: We have to find out the derivative

Q: 3. Solve the following using Two Phase Method MIN Z = x1 + x2 subject to 2x1 + x2 >= 4 x1 + 7x2 >= 7…

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Q: Solve the given initial-value problem. x1' = 2x1 – x2 – 4x3 + 2e¬t x2' = 2x1 – 4x3+ 3e¬t X3' = x2 –…

A: Given: The initial-value problem, x1'=2x1-x2-4x3+2e-t x2'=2x1-4x3+3e-t x3'=x2-2x3+e-t such that…

Q: In the function given. Evaluate the integrals.

A: ∫36-3gxdx=∫36-3dx·∫36gxdx Also, ∫36gxdx=1

Q: Find the general solution of xy²dx = e

A: By using variable and separation method

Q: Solve the higher order initial-value problem f''(x) = x-1/x + 3 ; f'(1) = 3, f(1) = 0

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Q: Show that y = x (1 – e*-1) is a solution | to y" – y' + e"-1 = -1

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Q: 4- (x2 + y2 + x)dx + xydy = 0

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Q: | √x dx 1 + √x A. x-2√√x+2ln (1+√x) + C 3. x-2√√x-2 ln (1+√√x) + C C. x-2√√x+2ln (1+√√x) - 3+C D.…

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Q: 2. Solve the initial value problems using separation of variables. a. x' = t²x² , x(0) = 1 x(t) = t…

A: Given equation is dxdt=t2x2            (i) By using separation of variables,…

Q: Find the real-valued solution to the initial value problem -3 x'(t) = x(0)

A: Given: X't=-32-1-1x and initial value is X0=1-2

Q: The solution of x¨ = kt with initial conditions x (0) = 1 and x˙ (0) = - 1 is given by

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Q: Integrate the function. 6x2 + 25x - 15 dx X(x- 1)(x+ 3) x(x-1) + C (X+ 3)3 ,5. O A. In О В. In x°(x-…

A: Integration

Q: 1-S dx ; 1-e-2x y2 + 2r +

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

Q: x(y-3). * - xly-3) dy = x(y-3)dx nly-31= C y-3 e [y-ce 3 2. Pesticide was given to a colony of 8000…

A: we have been given an equation y'=x(y-3) which can be written as  dydx=x(y-3) here, we will use…

Q: 10. f (Se e-3x XE -3e*-4e*)dx 4e)dx e-2

A: Solution: The expression can be written as

Q: 4- (x2 +y2 + x)dx + xydy 0

A: Differential equation

Q: -1 x-x2 dx -8 2도 1423 1521 22 20 Option 1 Option 2 1425 1523 22 20 OOption 3 Option 4 None of the…

A: Given problem:-

Q: Find the general solution of: (x² - y2)dx + 2xydy = 0

A: Here we have to solve the differential equation.

Q: solve the initial value problem dx/dt= x-x^3 with x(0)=x0

A: From the given statement, the initial value problem dx/dt =x – x3 with x (0) = x0.

Q: The equation of motion of an object of mass m, with initial velocity v(0) = 0, falling in air at a…

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