2ex/2 dx = 0 1 (e-1) 1 (e-1) e 1 2(e-) 4(e

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Q: sinh-1 x dx

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Q: Sin () dy %3D XCSC

A: Given sinyxdydx-1=yx cscyx, y(1)=0 Dividing both sides by  sinyx dydx-1sinyx=yx cscyx1sinyx…

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A: Find derivative

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A: Given differential equation is: dydx=x-20x Apply variable separable form to the given differential…

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A: In Variable separable separate the variable of x and y to LHS and RHS and then integrate on both…

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Q: V3x-e2x-(x ln x)(ln(ln x))| In(ln x) Given a function, y = dy Show that dx V3x-e2x (x In…

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Q: 10. (2х + Зу — 5)dx + (3х — у — 2)dy %3D 0 hint: Ca

A: We are asked to solve the differential equation.

Q: dy %3D xp 1-

A: We have to solve the Bernoulli differential equation :  dydx + yx = xy4

Q: 2-3 Find an indefinite integral: -dx 22+1

A:

Q: Ordinary differential equation dx/dy = ( x-e-x )/( y+ey )

A: We can solve as follows

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A:

Q: IntegrateIn(a) da. о х5 5 x5 ln(x) - x5 25 x5 In(x) - - 25 x4 5 ·ln(x) + 1 X - x5 5 x5 25 +C + C + C…

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Q: sin x) sin(x) +1 dy What is the general solution to the differential equation dr A y= sec(x) tan(x)…

A: Given : Differential equation dydx= sinxsinx + 1   To find : General solution for the given…

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A: Given that

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A: Given, xdx- √(a²-x²)dy=0

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A:

Q: olve The differential equation at ut+ut

A: First order differential equation:A differential equation establishes a relation between function…

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A:

Q: Basic Integration (x²-6++4) dx

A: A polynomial in the variable x is a function of the form anxn+an-1xn-1+···+a1x+a0. This polynomial…

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Q: he diff dy -1 dx

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Q: 1+sin x 7. y = in+sin x+ cos.x 8. y = In(In x) 9. sin y = In(x + y) 10. y = log(x sin x) %3D %3D

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Q: er differential equation by Va (D2 + 9) y = sin 3x

A:

Q: 0. 2+5x)e3 dx

A: Part a,

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A: Express the tan^x=sec^2x-1 and integrate

Q: dy Solve the differential equation: da tan (x). The curve passes through point (0, 0).

A:

Q: integral (1-3 square root of x)dx=

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Q: integral of x^2/x^2-5x+6 dx

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Q: Intergral x e^x dx

A: To find the integral (xexdx)

Q: Scoth (2) dx

A:

Q: cosh-1 x dx CO: хах

A: Let the given integral be y - y = ∫cosh-1x dx y = ∫cosh-1x1 dxIntegrating by parts - y =…

Q: dx 5. x + 1²x sin t %3D dt

A: Given ordinary differential equation is: xdxdt+t2x=sin t We have to solve the above equation.

Q: dy 5. dx — ху + хе**

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Q: Using Monte Carlo, estimate the value of eTy dx dy.

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Q: dx Show that a solution of the differential equation is y = (1 + 2x) sin3x Sketch the graph of y(x).

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

Q: Solving berneulli differential equation dy Xp

A:

Q: sinh-1 x dx.

A: We can find the answer as below

Q: linear differential equation dx/dy=1+2xcoty

A:

Q: Exact differential equation 2(у + 1)e?dx + 2(e* — 2у)dy %3D 0

A: Please see the below picture for detailed solution.

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A: Given,∫sinhe-xexcoshe-xdx

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Q: SOLUTION USING BY GAMMA FUNCTION Evaluate x/2 e dx.

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Q: (x? + Зу?)dx — 2хydy

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Q: 2. v = e-sinx

A: Given