Solve the Initial value problemy+2 (t) = e ++2) u3 (t) O b. y(t) = ee+3)2(t) %3D c. y(t) = e t- 3)u3 (t) d. y(t) = e 3(t-2)u3 (t) С.

Q: Solve the pollowing: り ( 2+J(xtjy) X=? ye! (b) (2+j)(3-j2) = a+jb a:? b:? (C) (メ-j2y) -(y-jx)-2j x=?…

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Q: 1. (2x-y) dx +(4x+y-6)dy=0

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: The general solution of (D³+4D)y=0 is (A) Ay=c₁еx+c₂e²x + c3e² (в y=e*(c₁cos2x+c₂sin2x) -4x y =…

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Q: What is the general solution of xy(xy5-1)dx + x²(1+xy5)dy=0 ?

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Q: Solve the Cauchy euler equation d³y x3 dx3 3x2 d?y dx2 2 + 6x -6y = 3 + Inx³ dy dx

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Q: 19. Find the general solution of (D4 + 6D³ +9D²)y = 0. 2 a. y=C₁ +C₂x+C3x² + c4e³x C46 Y = C₁ + C₂x…

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Q: (D² + D)y =x+| ;

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Q: Solve the ODE (e³ + 1)²e-³dx + (eª + 1)³e-ªdy = 0, y(0) = − = -4 by separation of variables.

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Q: y3 (x+c)e* is a solution of y-y3e"* A True B False

A: To show y=(x+c)e-x                     (1) is a a solution of y'-y=e-x                      (2) Then…

Q: y-3y" + y' + 5y =

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Q: 1. (2л + 5у)dA %3D? D YA (0, 4) у 3 (x + 2)2 X = y - 16 D (-2, 0) (0,-4)

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Q: 4. (D2 + 2D + 1Jy = 6

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Q: 3. Find the general solution of 2ху? + 4 %3D 2(3 — x?у)у'. А. X2у2 + 4х — бу %3D С B. x²y? – 4x – 6y…

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Q: The general solution of (D-4D)y-0 is (A y=c+ cx + Cze tk ® y-(c, + cx)e* +c3e* © y-c+ cx +Cye" -4x D…

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Q: Solve the equation (x + 2y-4)dx - (2x + y - 5)dy = 0. (x + y - 1)² = c(x-y-3) (x-y-1)² = c(x + y -…

A: x+2y-4dx-2x+y-5dy=0

Q: Find the general solution of y" = x-1 A. y = xln x – C1x + C2 B.y = xln x – C1x - C2 C.y = xln x +…

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Q: iv) if zy = (x)-1 then zx + Zy = %3D a. x – y b.x + y c. -z2(x + y) d. z²(x – y)

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Q: Find the general solution of (y + 1)dx + (4x - y) dy = 0 Show your solutions on a separate sheet of…

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Q: (Зху — 4у — 1)dx + x(x — 2)dy 3D 0; when x — 1,у %3D 2

A: According to  given Bartley guidelines to solve only one question at a time if it is not mentioned…

Q: Q.8 If v = (x² + y² + z?)¯/2, prove that a2v + ду? = 0. ax2 az2

A: We find second  the partial derivatives lf given function with respect to x, y and z and then add to…

Q: Solve the following DE using the method of undetermined coefficients: а. у"-Зу'+2у%3D20хе Зх b.…

A: To find - Solve the following DE using the method of undetermined coefficients : y'' - 3y' + 2y =…

Q: (c)2a) (c)(n)(z)(z) = e/(a) (c)(K)(z)) ¹/2 (b)(y) (6)(x) (y) Solve for K [(g) (m) (f)(K)

A: We have to solve for k.

Q: 3X (02-60,9)y=e" (x+2) %3D

A: Given differential equation is  (D^2 - 6D + 9)y = e^3x(x+2)

Q: 7. Find the general solution: y(x? + y²)dx + x(3x² – 5y²)dy = 0 a. y³(y² – x²) = cx b. 2y3(у2 — х?)…

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Q: Let f(x) = x² - 3, g(x) = Vx+1, h(x) : x+2 3 j(x) = -3x-5 %3! Determine the followings: ) f(g(3)) b)…

A: Here we want to find the composition of the given function.

Q: If r2+ 2r –1 = 0 is the characteristic equation of a homogeneous D.E. with constant coefficients,…

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Q: 3. 2хydx - (3xу + 2y?)dy %3D0 o (x - 2y)*(2x +y) = c O (x - y)*(x + y) = c (х + 2y)(2x - у)*- с о…

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Q: 5. Find the general solution of (D³-D)y=4e*+3ex. Ans. y=2xe*+(1/2)e2+c1+c2e*+c3e*

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Q: If E(X) = -2 and V(X) = 6 (i) E (5X – 2) = 5 E(X) – E(2) = (5 x (-2)) – 2 = -12 (ii) V (5X – 2) = 52…

A: As we know that Var(X)= E(X^2)-[E(X)]^2 This implies E(X^2)= Var(X)+[E(X)]^2

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.