The general solution of v" - y" – 2y' = e3t is: Select one: а. y(t) = c1 + C2 e21 + C3 e¬1+ b. y(t) = c1+ c2 e21 + C3 e- С. vle) = c, + Cz e?t + cz e¯1+e3r ,2t 12 d. v(e) = c; + Cz e?! + Cz e¯t –- ,2t 4

Q: Q6. Find the general solution of the equation: (mzny)p + (nx - ly)q = ly - mx

A: Identify the given partial differential equation and write it in the standard form Pp+QThe given…

Q: C e²cos (z² + 4) z²+9 -dz; C: |z2| = 2

A: Given ,      ∮C ezcosz2+4z2+9dz    ;  C: z-2=2 (.)  Cauchy - integral formula : let  'f' be an…

Q: Q2: Solve T" – c? uT = 0 given c = 3 and u = -1?

A: First I have put the given values into differential equation and then by method find the solution.…

Q: and ¹(w) = 2 × 4Sin ( 2 720 2w

A:

Q: Solve the equation: y" - y" -2y' = 0 Oy=c₁e* + c₂ + c3e²x y = ¢₁e²^³ + c₂e³ + c3e²x O

A:

Q: 1. Solve ,analytically. the Following differencetegs y(k)+ y(k=)-니3 Ck-2)-4y(e-3).=u(k).…

A: (a) Take the Z-transform on both sides of equation.

Q: [C: (B-ỹ)- B · (Č - )]Ã= (ỹ × Ã) · (B x C).

A:

Q: 4.) A particle's motion is represented by the position equation s(t) = t²-t, t≥0, where s is…

A: Solution:A particle's motion is represented by the position equation s(t) = t² - t, where s is in…

Q: d?y Find dx2 x = t° - 7, y =t - t?

A:

Q: 3) + 2x³y = y³x3 dau

A:

Q: r (Va² + 1 – Vr² – 1) Var4 – 1 To 1.

A: the given integral is: ∫510xx2+1-x2-1x4-1dx we have to evaluate the given integral.

Q: iv) if zy = (x)-1 then z, + Zy = b.x+y c.-z (x+y) d.z² (x-y) a.x-y

A:

Q: Sx2.- cos³ x-5 du 1-sin? x

A: Evaluation of the integral, bu using integral by parts

Q: 7 P ( 7 2 + b ) (F - ₂7 ) {

A:

Q: - 9x²y² = 3x²(1 – 3y²) + 3y dx3

A:

Q: xi+yj+zk Q5/ If F = find curlF.

A:

Q: = -21e 2 C D +4 D +9D t1o)y 4. /f x-O -4 l 10

A: To sove the initial value problem for y=y(x)

Q: Obtain the general solution: 1. (D² + 6D + 9)y = 18e 3* -3x

A:

Q: dz (9-z2) 2 Select one:

A: We have to find the integral.

Q: Σ 2 e-n? n=1

A:

Q: If f(x, y2) = x2 + y² + Vxy find: and (x?y) ду af(x²y) ax

A:

Q: w(r) = Vr4 + 4| dw dr

A: Given :   To find

Q: 2r² + 3sr - 2r t6s)s t s(st 2r -1) dr = 0 %3D

A:

Q: 6.) [D³ + 6D² + 11D +6] (y₂) = 0 7.) [4D³ + 4D² +D] (ro) = 0 8.) [D¹ + 2D³ + 10D²] (y₂) = 0

A: (6)…

Q: G1 G2 G3 G4 Which of the given graphs contains an Euler path?

A: Given three graphs G1,G2,G3 & G4.

Q: Find с dz 23 (2+4) > where C: 13+21=3.

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.