Show that y = c1ex + c2e-x + c e + 3 is a solution of y ||| -2y | | - and | + 2y = 6 (justify).

Q: Q2) The general solution of y" + 2y"-y' - 2y = 0, is: a) y(x) = c₁e²x + ₂x + c₂e* c) y(x) = c₁e²x +…

A: Solution :-

Q: 4. Find the particular solution of xy' – 2y = -x ; when x = 1, y = 5 a. y = x + 4x² b. y = 2x + 3x²…

A: xdydx-2y=-x⇒dydx=-x+2yx⇒dydx=-x+2yxPut…

Q: A. Find the general solution of the DE: y" - 2y' +y = 6e'

A: Given A. y"-2y'+y=6et

Q: Verify whether y(x) = 2e-*+xe-* is a solution of y" + 2y + y = 0.

A: Topic = Differential equation

Q: Find the particular solution of x²y" + xy' = 1; y = 0 and y'= 1/2, when x=1.

A:

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

A: According to company rule we can answer only first question and rest can be reposted.

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…

A:

Q: ) Obtain the general solution of y" + 2y + y = e² In r

A: In this question, the concept of the differential equation is applied. Differential Equation A…

Q: find general solution. dr/dt= -2tr,         r(0)=ro

A:

Q: - Find the number of non negative solutions to x + y + z = 21.

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Q: Solve a & b with given A[r = 3x şax+ (y + z + 3) Ay +(6x - z³) a₂] where: np = ax + 4ay - 2az 2+y³

A: Given

Q: The solution of y = 5y + e 2"y2, y(0) = 2 satisfies:

A:

Q: Find the general solution to t²y" +2ty' - 2y = 0 given that y₁ (t) = t is a solution.

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Q: The particular solution In (x) = 3x + 4y, y(0) = 0 is A. e³x + 3e-4y = 4 B. 4e3x3e-4y = 3 C. 4e3x +…

A: Topic = Differential equation

Q: Q3. Verify that y² = x² – 3 is the particular solution to the following ivp: y' = ; y(2) = -1. %3D

A: To check whether a solution is particular solution to ivp , it must satisfy the differential…

Q: Give a particular solution for y" – 2y' + y = 1+x2

A: Given that a differential equations - y" -2y' +y = ex/1+x2.   We know that integration of 1/(a2 +x2)…

Q: Find the particular solution of the DE y''-11y'+24y=0 when y(0)=2 y'(0)=-3

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Q: Show that y %3D Cіx-1 + С2х + Cзlnx + 4x2 is a solution to x3y" + 2х?у" — ху' + у %3D 12х?.

A:

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

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Q: 2. Verify that e 2 is a solution of the equation y" -3y'+2y=0.

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Q: Check that y Cx) = e* is the Solution of y" + y' - 2y = 0

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Q: What is the particular solution of (2ay? + 3x?) dæ + (2æ²y + 4y³dy ) dy when 2 and y 1 O x? y? + x³…

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

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

A: Explanation of the answer is as follows

Q: 8. What is the particular solution of 2xyy' =1+y², when x = 2, y = 3 ? а. у%3D5x -1 C. y =V5x + 2 b.…

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Q: (D² – 3D + 2)y = e2×(1 + e2x)¯ -

A: Given: D2-3D+2y=e2x(1+e2x)-1 Formula used:y=yh+yp

Q: What is the general solution of xy^2dx+x^2ydy=0

A:

Q: Find the general solution to the DE y"-4y'+13y=0

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Q: 7. Verify that y = x2 - 1 is a solution of (y')* + y? = -1.

A: Given- y=x2-1 To verify- That the above function is the solution of y'4+y2=-1.

Q: 3. Verify that 3e 2x + 4e* is a solution of the y"-3y'+2y=0.

A: We have to verify if the given is a solution to given differential equation or not.

Q: ) Give a particular solution for y" – 2y' + y = 1+x² *

A:

Q: What is the particular solution if y(1)=0? 1/2 xy = y + (x² + y³)"

A:

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: Obtain the particular solution of x²y" + xy' = 1; y = 0 and y' = 1/2, when x = 1

A:

Q: The particular solution of xyy' = (x² + y²) when x = 1, y = 2 is a. y2 = x² In x² + 4x² b. y2 = x In…

A: Given:- xyy'=(x2+y2)  To find:- Particular solution of given differential equation when x=1 and y=2

Q: 8. Find the particular solution of x²y"+ xy' = 1; y = 0 and y' = 1/2, when x = 1.

A: eular method

Q: Q2. Find general solution of the DE 4y" + 4y" + y' = 0

A:

Q: Find the general solution of the x²y" + xy' − y = 3x, x‡0;

A: *By Bartleby policy I have to solve only first one as these are all unrelated problems.These are all…

Q: (b) Show that for x > 0 and k + 0 the equations In x x* = e* and 1 have the same solutions

A:

Q: 2. obtain the general solution. a.(D - 3D + 2)y = 2x – 9x2 + 6x. b.(D2 + 4)y = 5e - 4x. c. (D² + 4)y…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

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

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Q: Is y = 1/(x + C) a solution to y' = -y^2?

A: To solve the following differential equation.

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

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Q: 5. The particular solution of y' + y = y¯² when x = 0,y = 2 is

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Q: c) give a particular solution for y" – 2y' + y = 3e* + 1+x

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Q: 5. Find the general solution of y"' + y'" - 6y' + 4y = 0 +

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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 of: x² = y² QY_ dr

A: We have to find general solution of given differential equation.

Q: The particular solution of y' - y = -x when x = 0, y = 3 is a. y = 2x + 3e* + 2 b. y = 3x + 2e* + 1…

A: This question is based on first order differential equation.

Q: 4. Verify that y=cx+e² +1 is a solution of the equation y=y'x+(y')' +1.

A: