Find a particular solution for i= -3y - 4 + Se ya- Sya + 6ya - 6e (0) - 19, ya(0) - -23

Q: Find a particular solution to y" + 8y' + 16y : -7.5e 4t t² +1 Yp =

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Q: Q1: find the complete solution of the following: 1. y" + 4y' + 4y = x2 e-2x

A: Given equation- y''+4y'+4y=e-2xx2 Auxiliary equation- m2+4m+4=0m+22=0m=-2,-2

Q: Find the solution. xy'- xy = 1- y, y(1) = 0 A y --(1 - el-) © y -1+ el+")

A: Solution of the differential equation

Q: 2 Find the particular solution of y' +y = -x°y5 ; У(-1) %3 2

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Q: The solution of the IVP y = x2(1+y), y(0) =3 is O None of these. y= 4e 3 - 1. y3 xe + 3. .3 3. y36e…

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Q: 3. Prove that the solution to the equation 9yy + 4x = 0 can also be written as: y2 = c: and what is…

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Q: What is the solution of the given equation valid near the origin for x>0? x2y''+x(2+3x)y'-2y=0

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Q: Find the general solution of the following IVP: y"- 2y' +y = 0 ,y(0) = 5, y'(0) = 10.

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Q: Find the solution of y"-y'-6y = -e* +12x with y(0)=1, y'(0)=-2 by method of undetermined…

A: The Auxiliary equation is D2-D-6=0 Solve for D  D2-3D+2D-6=0DD-3+2D-3=0D-3D+2=0D=3,-2 Therefore, the…

Q: The solution of the DE (4xy -3)y' =-2y² -1 is 2xy² + x – 3y = c O None of these 2хy? - х - Зу 3 с…

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Q: Show by direct substitution that (-1)"+1 y = n-1 is a particular solution to (x + 1)y" +y' = 0

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Q: The solution of the following IVP:y' =y3 x e*, y(0) = 1 Select one: a. y=V4-2 ex2 O b. y=V2-ex? O C.…

A: Given IVP is y'=y3xex2, y0=1 We have to find the solution of the given IVP. Now y'=y3xex2…

Q: Find the solution to x' = y y' = 12x + 1y if x(0) = 0 and y(0) = 8

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Q: The value of A for which the equations 2x + y + 2z = 0 x + y + 3z = 0 4x + y + Az = 0 have non-zero…

A: Let us consider the system of homogenous system of equation AX=0 The Solution of system has Zero…

Q: Find a particular solution to y" + 5y + 4y = -10te". Yp =

A: Given the D.E. y''+5y'+4y = -10te3t We have to find particular solution yp of this equation.

Q: Determine the particular solution. 4y/"- 2y- 2y-0; y (0) 2, y (0)-1 O y = (4/3)e(x/2) - (2/3)e* O y=…

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Q: Find the solution of y' + p(x) = 4x if y(0) = 3 and where

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Q: Find the general solution to y" – y' – 2y = 3x + 4. (Be sure to find the values of the coefficients…

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Q: 10. Find the particular solution that satisfies the initial condition. my'+2y = 3x2-5x, Initial…

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Q: Determine the particular solution for y"-4y'-12y=2t^3-t+3

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Q: Find the particular solution of r*y – y y+1 ; y (3) = -1

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Q: 2y'' + 3y' = 2cos(3x)

A: To find  The general solution for 2y'' + 3y' = 2cos(3x)

Q: Find a particular solution to y' – 2y + y = -13.5e". Yp

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Q: Give a particular solution for y" - 2y' + y = 3e".

A: Explanation of the answer is as follows

Q: Find a particular solution to y" + 6/ + 9y = 3.5e 3. Yp =

A: Given thay  y"+6y'+9y=3.5e^(-3t) To fin the particular solution

Q: Find the particular solution: y" + 16y' = 0, when x = 0, y = 0, y' = 0, y" = 1

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Q: The particular solution to y" + 2y' + y = x is: Select one: а. 2х-2 b. 2х- 1 С. d. X- 2

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Q: Find a particular solution to y"+3y'+2 y = x² - 3.

A: Given that,         y"+3y'+2y=x2-3  ⇒D2y+3Dy+2y=x2-3 Where, D=dydx ⇒D2+3D+2y=x2-3  Let, FD=D2+3D+2…

Q: Find the solution. y' = 5y + e-2x y-2, y(0) = 2 -15x 13e A) y = + 3e 2r1/3 23 139e 15x – 3e -2x \1/3…

A: Given differential equation is in the form of Bernoulli's differential equation.

Q: 4. Find the solution of the following DE: a. y(5) + 5y(4) + 10y(3) + 10y" + 5y' + y = 0

A: Given differential equation is: y5+5y(4)+10y(3)+10y''+5y'+y=0 Write auxiliary equation corresponding…

Q: The general solution of the DE: y" – 3y = 0 is Select one: y = ce² + cze³z y = c +cze³z y = ce² +…

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Q: Find the general solution of the following DE. y' = 3 (y + 1) O y = 3ce³x - 1 Oy = ce³x - 1 Oy =…

A: y' = 3(y+1) dy/dx = 3(y+1) dy/3(y+1) = dx dy/(y+1) = 3dx now apply both side integration

Q: Find the general solution: ydx-(e^у+2ху-2х)dy О А. ху^2-се^2у+2(y+1) е^у О в. ху^2-се^2у-2(у+1) е^у…

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Q: ) Find the general solution to y" – y' – 2y = 3x + 4. (Be sure to find the values of the…

A: i have find Complementary function and particular integral, the general solution is the sum of them.…

Q: Find a particular solution to -18.5e-2t y" +4y +4y = 12 + 1

A: Introduction: A differential equation is an equation that contains the derivative of an unknown…

Q: Find the general solution of the following: 1. (D² – D – 2)y = 0 2. (D² + 3D)y = 0 3. (D² – 5D) + 4y…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Consider the following IVP: y'' -3y' -10y = 1, y(0) = -1, y'(0) = 2

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Q: Find a particular solution to 16.5e-2t t2 +1 y" + 4y' + 4y Yp =

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Q: Find the solution. y' = 5y + e2x y-2, y(0) = 2 13e-15x + 3e2x )1/3 A y = 23 139e 15x – 3e -2x )1/3…

A: Giving differential equation is  y'=5y+e-2xy-2 , y(0)=2

Q: 4. Find the solution for the following y""+y"+ 2y = 3 y(0)= 1, y(0)=1,y)=1

A: Solution :-

Q: Provide general solution of the given ay'' + by' + cy = 0and b^2 - 4ac < 0

A: Solution: Consider the given differential equation is ay'' + by' + c y = 0 or aD2+bD+cy = 0   where…

Q: 3. Find the general solution of the following DE. y' = 3 (y + 1) O y = ce³x - 1 3y = ce³x - 1 Oy =…

A: Use variable separable to Solve this problem.

Q: Find the general solution of the following DE. xy² (y')² + y(x - 1)y' - x³ = 0

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Q: Find the solution. y' = 5y + e 2x y2, y(0) = 2 -2х 139е 15 — Зе - 3e -2x \1/3 A y = 17 15х 19е 15x _…

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Q: Find the particular solution of y" + 2y' – 3y = 0 when x = 0, y = 0, y' = -4. %D

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Q: b) Find particular solution of х*у 3- (х-1) у. У(1) — 1. У(1) %3D 1.

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Q: find the particular solution of y" + 12y'+36y=0 with y(0)=3 and y'(0)= -36.

A: Given differential equation is: y''+12y'+36y=0 Auxiliary equation for the given differential…

Q: If y₁(x)=e³x and y₂(x)=xe³* are solutions to y" - 6y' +9y = 0, what is the general solution?

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Q: Find the general solution: x(x^3-ху^2+2y^з јdу-убх^3+2у^3 jӑх-0 О А. 4ху^2 In [y+x^3-2y^3-2сху^21 О…

A: Explanation of the answer is as follows

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.