1. If x'y" + xy' + (x². 4 - -y=0 Y=x sinx , and y= y,v. Which of the following x>0 equations satisfied by v Select one: a. (x 2 sinx)v" + (2x 2 cosx)v' = 0 b. 1 (x 2 sinx)v" +(2x 2 cosx-x ?sinx+ x sinx)v' = 0 C. (x 2 sinx)v" +(2x 2 cosx)v= 0 d. (x sinx)v" + (2x 2 cOsx)v' = 0

Q: y" – 9y = t° – t e + sin(3t)

A:

Q: Solve ( sin θ - 2r cos^2 θ) dr + r cos θ ( 2r sin θ + 1) dθ = 0 a. r sin^2 θ - r^2 cos^2 θ = c b.…

A: Given that sinθ-2rcos2θdr+rcosθ(2rsinθ+1)dθ = 0. The objective is to solve the given equation.

Q: 4). Evoluate 2. (88e0 COS X cot x)dx 4

A: Definite integration

Q: Eliminate 0 from the equations : (i) x = h + a cos 0, y = k + b sin 0 (ii) x = a ser³ 0, y = b cot³…

A: Solution is given: Hope the solution is helpful.

Q: 38. Differentiate y = 2 cos² - a. – sint b. - sin 2t C. - sin - d. sin-

A: Differentiate y=2cos2t2

Q: Solve csc y dx + sec²x dy = 0 elect one: a 4cosy + 2x - sin2x = c O b. 4cosy + 2x + sin2x = c c.…

A:

Q: If x'y" + xy'+(x? -y=0 x>0 ,y,=x 2sinx , and y=y,v. Which of the following %3D equations satisfied…

A: Let   y1 and y2be two solutions of the second-order linear differential equation d2ydx2+Pxdydx+Qxy=R…

Q: b) Solve to find if y = Tant VE and t = 4x-2 – secx dz b) if z = sin20, and 0 = [cos(w) + 1]² + cos…

A:

Q: Find all complementary functions of the equation y" - 4y' + 4y = 0. a. cos2x, sin2x b. e-2x,xe-2x C.…

A:

Q: find all values of unknowns which satisfy the following equations: 1. (x, y, z) - 3(-1, 2, I) = (0,…

A: Since you have posted a multi subparts question according to guildlines I will solve first three…

Q: If x'y" +xy' + (x2 - -0 x>0 , V1=X 2 sinx and y=y,v. Which of the following equations satisfied by v…

A:

Q: y" cot x + (cotx) In (sinx). Show that Cscx %3D 2y - 3 cotx. %3D

A: given function :y= cotx+(cotx)lnsinx

Q: If x²y" + xy' + (x² – ÷)y=o x >0 ,V,=x 2 sinx , and y =y;v. Which of the following equations…

A:

Q: 4. sin (5x + 22) = cos (4x + 14). Find x.

A: Equation is given by                sin(5x+22)= cos(4x+14)   ---(1)       formula which is to be…

Q: 5. 4 (secx-1)(sec² x+secx+1) Sª cos² 2x-2 cos 2x+1 -dx

A: Indefinite integral is the process through which one can determine the function which on…

Q: Yp = A1 cos V2t + A2 sin V 2t Which of the following is Yp'? sin v2t A1 V2 Cos /2t A2 V2 O V2A1 sin…

A: Please see the explanation below

Q: V. Find the third derivative: 1) y = 10 tan(x) - 2 cot(x) 2) y = x³ - x² sin (x) 1 3) y = 2 sin(x)-4…

A: The given problem is to find the 3rd derivative of the given functions.

Q: 1 = x²y" + xy' + cx? - +»v=o x>0 ,V1=X sinx , and y =y,v. Which of the following quations satisfied…

A:

Q: If x³y" + xy' +(x? -y=D0 x>0 ,y,=x sinx , and y3V,v. Which of the following 3 equations satisfied by…

A:

Q: Find the solution. y'= 1 + 3ytanx (A) 3y tan³x=c+ 3sinx-cos³x B 3y cos³x=c+3sinx - sin ³x D 3y…

A:

Q: 1-) 2csc23x 1-S sec3xVsin3x

A:

Q: sinxcos ydx + cos²xdy=0

A:

Q: Solve y = x - 2ycot2x A B (C) D 2xsin 2x + (4y - 1) cos2x = C (4x - 1) sin2x + 2xcos2x = C (4x − 1)…

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Q: (1 point) Check by differentiation that y = 3 cos 2t + 3 sin 2t is a solution to y" + 4y = 0 by…

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Q: sin3xdx Cos4x

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Q: Ir x²y" + xy' + (x? - +>v =0 x >0 || | 1 - 2 sinx ,V1=X the following equations satisfied by v and y…

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Q: Evaluate (tanx * dy/dx) - у %3D а a. y = -a + C(cscx) ОБ. None of the choices О с. у%3-а+ C (cosx) O…

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Q: 6) y = (sin¬1 8t) (sec -1 derive

A: First, we use the product rule

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A: Given query is to find the derivative of the expression.

Q: If 00 and csct>0 C. cos t0 b. cost>0 and csct0 and csct>0

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Q: 1- cos 4x 9. sec2 2x – 1 = 1+ cos 4x

A:

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.