Solve the given differential equation by separation of variables. ху + 5х — у —5 ху — 2х + бу-12 We first factorize dx ху + 5х — у — 53(х+| —1 )(y+ 5 ху — 2х + бу — 12-(х+| 6 )(y+-2 ソー2 ア+5 х —1 And then we separate the variables dy= dx x +6 The solution to the differential equation is

Q: Solve for Differential Equation 4y"-4y'+37y=0 when y(0)=3 and y'(0)=1.5

A: Given differential equation is  4y"-4y'+37y=0 Initial condition is y0=3, y'0=1.5

Q: Solve the differential equations (t - 1)3 ds/dt + 4(t - 1)2s = t + 1, t > 1

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Q: Solve the differential equation: y" – 21y' – 72y = e24= 1 e24x 24 -3z y = C1e + Cze²4z Oy = Cje-3 +…

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Q: Given that y(2) = 3, what is the particular solution of the differential equation y = 6x? + x -5? a…

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Q: 5. The order of the differential equation (y" )5 + 2x(y"')* – 3y' - 4x° = 0 is c. 3 d. 6 a. 5 b. 4

A: Topic:- calculus

Q: 1. Find the solution of the given differential equation using any method. y" – 3y' + 2y = 2x2 + e* +…

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Q: Solve the differential equation y" +3 y' + 2.25y = -10 e-15x %3D y(0) = 1, y'(0) = 0 by using…

A: Consider the equation:y''+3y'+2.25y=-10e-1.5xy(0)=1, y'(0)=0Consider the homogenous…

Q: The solution of a differential equation is y=c₁e4x + c₂e2x, the differential equation is given by…

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Q: Give the general solution of the differential equation -5x y"+ 10y'+ 25 y =3xe a) O y=C, e*+ C,xe…

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Q: (b) Find the complete solution of the differential equation y" + 9y = -5x² + 4cos2x %3D

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Q: Solve the higher order differential equation y(3) + 4ÿ – 5ý = 0 , y(0) = 3,y(0) = -5 ÿ(0) = 9 A:y =…

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Q: solution of the given differential equation 2x^3y' = y(y^2 + 3x^2)

A: Given differential equation is,  2x3y'=y(y2+3x2)⇒dydx=y(y2+3x2)2x3

Q: 4 2. y'--y=-2y² In x

A:

Q: Determine the solution of the differential equation y' = 2y + x2 + 5 1 1 X- 2 11 -2 X' 2 + Ce-2x а.…

A: Given: y' = 2y+x2+5 dydx-2y=x2+5   Linear differential equation is of the form dydx+Py= Q, where P…

Q: Solve the given differential equation by undetermined coefficients. y"+y' + y = x² - 5x -2x Xx) =…

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Q: Solve the ff. differential equations by applying the appropriate substitution. dy = 2+y-2x+3 1) dx…

A: Since, you have asked multiple questions as per company guidelines, we will solve the first question…

Q: Given the differential equation + 9D + 27D+ 27) y= In(2x – 3). Propose an appropriate particular…

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Q: The order of the differential equation (y")5 + 2x(y"")* – 3y' - 4x2 = 0 is - а. 5 с. 3 d. 6 b. 4

A: Given Differential Equation: yvi5+2xy'''4-3y'-4x2=0

Q: Determine the particular solution to the differential equation given by: 3x2+4x-4 y' = ... 2y-4 if…

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Q: 4. у 3 2ах + bx2

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Q: Which of the following is a solution of the differential equation xy' + y = 4x? y = 2x - 7x-1 Oy =…

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Q: Solve the differential equation: (2y+3)y'=-(1-3t²)

A: Given that: (2y+3)y'=-(1-3t2)

Q: Find a particular solution to the differential equation Ур = -6y" - 5y'-y = -(t² + 2t + 2e²t).

A: To find a particular solution to the differential equation.-6y''-5y'-y=-t2+2t+2e2t

Q: Consider the differential equation Y+ 2y = 4x - 3e*, given that y(0) = 1 and y (0) = 2. What would…

A: Given, Y"+2y' =4x-3ex

Q: 3. Find the particular solution of the differential equation (y² – x²)dy – 2xydx = 0; when x = 4; y…

A: Given differential equation is y2-x2dx-2xydx=0                       (1) with condition , when x=4;…

Q: solve the given differential equation   7.    x2y" − 3xy' − 2y = 0   9.    25x2y"+ 25xy' + y = 0…

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Q: 2. Find the solution of the given differential equation using any method. (D3 – 4D² + 7D)y = -11

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Q: 4. 4y" - 5y' = 0 , y(-2)=0 & y'(-2)=7

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Q: 2. Determine whether or not y = Ce2t + C2e-4t + (4/7)e3t is a solution to the differential equation…

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Q: Solve the differential equation y' -2y =4-t Select one: 2t а. у%3-1.75 + се 2t b. y=-1.75 +0.5t + ce…

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Q: Which of the following is the general solution of the differential equation In()- x²+e5x) = -2y ? a.…

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Q: If yH of a differential equation is cje2* + cze3x + cze-3x, then W1 = %3D (a) 0 (b) 9 (c) 5e-* (d)…

A: If yH of a differential equation is c1e2x+c2e3x+c3e-3x, then we have to find the Wronskain W.

Q: Find a differential equation whose general solution is 7t y = c₁e¹t + c₂e-2t. y" - 5 y' - 14 y = 0 ✓

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Q: Solve the differential equation y''' - 3y'' - 4y' + 12y= 12e-t, y(0) =4, y'(0) =2, y'''(0) = 18

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Q: Given the differential equation, its particular solution, and its wronskian –7x y" + 2y' - 35y = 4…

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Q: Solve the differential equation y' -2y =4-t Select one: 4t a. y=-1.75 +0.5t + ce 2t b. у%3-1.75 + се…

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Q: Solve the higher order differential equation y) + 49 – 5ý = 0 , y(0) = 3.y(0) = -5 y(0) = 9 A:y =(e-…

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Q: Solve the differential equation y’’ – 4y’ + 13y = 0 with initial conditions y(0) = -1 and y’(0) = 3.

A: Given y''-4y'+13y=0 , y(0)=-1 &  y'(0)=3

Q: The solution of the differential equation x2y" - 2xy' + 6y = 0 (x > 0) is the function y(x) = C1…

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Q: The particular solution y, of the differential equation y" + 4y' + 4y 3x2 + 1 is (1/8) (1-2x+6x^2) O…

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Q: Solve the higher order differential equation y() + 4ỹ - 5y 0, y(0) = 3,y(0) = -5 y(0) = 9 A:y…

A: To solve the given higher order differential equation

Q: Solve the following first order linear differential equation: y' + 3y - (7x+1) = 0, y(0) = 2

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Q: One solution of the differential equation -y" + 7y - 12y = 0 is y = e3x. A second linearly…

A: Solution in step 2

Q: Which differential equation has y = Ae* +Be* - 2--x 2 as its general solution? Select one: O a.…

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Q: Find the solution of the differential equation у" — 4у — 4х — Зех - y = Ce2x + C2e¯2x + e* + x а.…

A: Solution:

Q: Solve the ordinary differential equation y'+4y-3x³, using Runge-Kutta method with Xe 0, Yo-1, X₂-2,…

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Q: Solve the following differential equation y"+2y'-15y 0 Select one: O a. y= c,e3x+ c,e-6x O…

A: we have , y"+2y'-15y =0Auxiliary equation is gives by :m2+2m-15 = 0⇒m2+5m-3m-15=0⇒m(m+5)-3(m+5)=0⇒…

Q: Solve the general equation and the unknown coefficients of differential equation if y(1)=2 and…

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Q: 3-  (a) solve the given differential equation  y''' - y'' -4y' +4y = 1-e^x  (b) without solving.…

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Q: –7 + 12 d5x 7) 25 d*x -7- dt5 d²x + 12 dt3 + 8. = 0 dt4 dt2

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.