Solve the linear D.E D Xdy (2y + 2x+ X²Jdx ニ 2) sinx dy + y cos X = 2sin? x Cos X D (x²+1) + 4x y ニ Ox (x2+1) 4) (1-x²) dy + 2xy = X Vi - x2

Q: Find the solution. 2y + =xy-sinx dx y = x²(cosx+c) 1 B y = r²(sinx – c) y = x²(cosx+c) D y = x(sinx+…

A: Given dydx + 2yx = x2y2sin(x)

Q: solle (1+ cos x) dx Sin²x dx (x-2)√√x² 4 X +3 1

A: The given integral is a complex integral involving trigonometric, polynomial, and radical functions.…

Q: 12 A A10. If B then the values of A& B =. %3D (x-2) (x+4) x-2x+4 A 2, – 2 b) -2, – 2 c) 2, 2 d) -2,…

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

Q: EVALUATE 3 x2 +1 cos dx -1 dx x2 +1 А. cos В. О C. 2/ cos 3 dæ x2 +1 D. 1

A:

Q: dly dx2 - 2 dy dx -3y = COS X

A: The given differential equation is d2ydx2-2dydx-3y=cosx. We have to find the solution of the given…

Q: 2 x+1 2) Evaluate f,“ dx using the substitution u 3 Зх — 2 V3x-2 3) Evaluate f2 e cosx dx

A:

Q: a. +4 cos x +6 sec x – 5 ) dx 2 x5

A:

Q: | w(w? + 1)3dw -1 dx х2 sin30cose d0

A: We will answer the first question since exact one wasn't specified, Please resubmit the question and…

Q: Qlif y= fcus and u=x46x +5 U =X and - 2u -1, Sind dy dx

A:

Q: Find if y = cos(e-2=) dy None 2e-2". sin(e-2") 3e2r. cos(e-2r) e2= . sin(e-2#)

A:

Q: One approach to evaluating 2 cos (2x)dx is to first rewrite it as cos(4x) + 1 dx а. cos(2x) – 1 dx…

A: This is the question of integration.

Q: fxcos 73 x cos 4xcos 2xdx π ſcos(nx)dx 75 ーπ 77 xsin(nx)dx

A:

Q: - 4x + 30 -dæ Evaluate (x – 5)(x + 5) + C

A: To solve the given integral first break the integrand into the simple expression using partial…

Q: 3. Integrate the following: 2x+3 i. J7+3x ii. S V1- cos x dx iii. S cos3 x dx

A:

Q: dx x4+16 Įtan-( x2 + c 4

A: Given that, ∫xx4+16dx

Q: S cos(7x + 5) dx = (sin(7x+5))/7 + c* O False O true

A: We have to evaluate   ∫ cos(7x + 5) dx

Q: 2 a. (1+5 ln x)³ dx fa+ b. (1+3 tan x)² sec? x dx 2x + 5 dx Vr – 3 2x3 – 5x? + 9x – 4 C. - d. dx x²…

A: Disclaimer: Since you have asked multiple questions; we will solve the first question for you. If…

Q: 12 cos√(√x+4 dx

A:

Q: Sy sin 3ydy

A:

Q: d dr -x² + e³¹ - tan(x) dy²-sin(y) dy cos(y) +2 d dx -√x+e²

A:

Q: Find The geneval Solution f 3y Cosx + 4x + 2x² e) dx + (3 Sinx + 3) dy

A: Here we have to find the general solution of the given differential equation which is of the form…

Q: 1. (D² - 4D+5) (e² sin x)

A:

Q: 3n 2n TE S. (sin x + cos y)e dx dy dz A. 2n(e2n + e3) B. 2m(e2 – e3") c. 2m(e + e2") p. 2n(e- e")

A: For the solution follow the next steps.

Q: 2n Sin (3y) dx + 3x Cos(ay) dly =o

A: Given differential equation is 2xsin(3y)dx+3x2cos(3y)dy=0

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.