Integrate the followings using appropriate approach 4 (a) 3z2 +1 dz 2 (z+1) (2- 5) (b) (3t + t²) sin(2t) dt.

Q: solve xsinydx+(x2+1)cosydy=0

A: Given differential equation is: x siny dx+(x2+1) cosy dy=0 Use variable separable method to solve…

Q: S(;+ sin(x) – Vx²) dx

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Q: y = x * (sin 1x)² – 2x + 2v1-x² * (sin-1x), Find dy dx

A: Given that equation of y and we find dy/dx. We know that d(sin-1x)/dx = 1/√1-x2. And d(xn)/dx =…

Q: find the general solution of  xdy/dx+4y=(sinx/x)*(sqrt of y)

A:

Q: ((x/y)/z)+(x/(y/z))

A: In mathematics, precalculus is a set of course that includes algebra and trigonometry to prepare…

Q: xsin ax 2 2 (x²-x²) 1/2 Show that [²= - dx - TV J₁ (ay) 2

A:

Q: -cosh(2x² + 1). Evaluate (A) 4xsinh(2x² + 1) B 2xsinh(2x²+1) C) xsinh(2x2 +1) с D (2x2 + 1)sinh(2x +…

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Q: Integrate S (2x+1) Staz+X+4) dx

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Q: csch (2 sin2x) dx 1. V1-4x² r(²-1)cos[cosh (In r)]dr OS 4.

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Q: S(6Vx + 3 cos x - 8)dx

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Q: Integrate (2x - 5) with respect to x from x = 2 to x = 5.

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Q: sinx

A:

Q: (x? + 3x — 45)dх J«+ 3)(х + 12)(4х — 3)

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Q: 4 fcos 3x sin³ 3x dx

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Q: Find ds/dt if 3t + 3s sin(3t) + 3cos(t) %3D

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Q: (D4 + 18D2 + 81)y = 0 (A y = (c, + c,) cos3x + (c,+c,) sin3x. (B у %3 (с, + сх) cos:3x + (с,+c)…

A: To solve the given differential equation first we construct auxiliary equation and then solving the…

Q: compute (x2 - 8x +20) dx on the interval (0,1)

A: To evaluate the given definite integral over the open interval (0,1)

Q: 故(x3+5) ex A al d Iny d in5x

A: According to our guidelines we can answer only three subparts, or first question and rest can be…

Q: (b) 9-(t+1) (42t - sin t)dt

A: Given that the integral is .The objective is to evaluate the given integral.

Q: 1. (D² - 4D+5) (e² sin x)

A:

Q: COs ax dx. x² + b² (q)

A: Cauchy residue theorem: If f is holomorphic function defined on simply connected open set with…

Q: Evaluate (i) dx S √e xlnx√(2lnx)² – 1

A: We are asked to evaluate the integral

Q: (2y + √y sin x) dx + xdy = 0

A:

Q: xdx 2x +3 a) Í b) s2*-2x-4 dx c) 2x' + 6x? +4x - dx x + 2x – 3 х2-1

A: As per our guidelines we can help you in solving only first three subparts. Rest of the problems you…

Q: Find The The Peeeeer genoval solution of (3y Cosx + 4x + 2x² ex) dx + (3 Sinx + 3) dy

A: The given  differential  equation  is  3ycos(x)+4xex+2x2exdx+3sin(x)+3dy=0.......(1) Now, (1)  can…

Q: Evaluate (i) [Hint: / 2xe" dx udv = uv - 3x (ii) dx x2 – 4x – 5

A: we have to find the following integral

Q: d?s sin 3t + cos 3t dt2

A: Explanation of the answer is as follows

Q: d^2y/dx^2 + 3dy/dx + 4y = 3x + 2 Utilize the indeterminate coefficient technique to solve the above…

A: Here is the, solution

Q: dr 21. (1+x²)/16 – (tan-l r)² dx e2x+2+2 22. 8. dx x2 - 6x + 25 23. 6. 24. dr J (2 - r)V - 4x +3 dr…

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Q: x° + 4x? dx (a) x² + 4x + 3

A: Due to our guidelines I am solving only first problem please repost other question. I =…

Q: 11 .7. Determine: / 3 (2 – 5x')"(7xº – 15a²)dr J 3x+5

A: We will evaluate the given integral.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.