4. ß (ß+ 30 +2) d0 + (oß +0²+0)dp =o

Q: Let y(x) be the solution for the DE: y = (x + y-1)? If y(0)– 1, then find y() 3元 O 2+7 O8-7 O 2-7

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Q: Solve the given DE y'= X - x 3 — 2y 3 3ху 2

A: We have to solve the differential equation

Q: Find a particular solution to： y''+5y'+4y=10te^(4t) y(p)=?

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Q: 7. Find the solution of the DE: (D? + 9)y = x+e2 using method of undetermined coefficients.

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Q: 5. Find a second solution to (1 – a2) y" + 2xy' = 0, given one solution y1(x) = 1.

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Q: y" + 5y/ + 4y = 4te*.

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Q: Consider the following IVP: y'' -10y' +9y = 5t, y(0) = -1, y'(0) = 2

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Q: Determine the general solution of  3(3x²+y²)dx - 2xydy=0

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Q: Find the general solution of the following DE in explicit form. y' =2+2/y-2x+11

A: Solution: The differential equation is y'=2+2y-2x+11 Suppose that v=-2x+y so that y=v+2x Then,…

Q: S¹₁₁ S1+₂x² x + 2y dy dx ·12x²

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Q: Let y(x) be the solution for the DE : y = (x + y + 2)2 If y(0) = -2, then find y() ○2-푸 O 8 - T O -…

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Q: 6. Find the solution of dy = (y² – y)x². dr

A: Definition used -          The solution of the variable separable differential equation-…

Q: If y=e' is a solution of the DE: ty"-2(t+ 1)y'+(t +2)y=0 Then the general solution of this DE is :…

A: The given differential equation is: t…

Q: Q2\ Find the general solution to the given Euler x?y – 3xy' + 9y = 0

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Q: Solve for the particular solution of the following non-homogeneous DE. y” - 4y - 12y = e6t

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Q: Find the particular solution determined by the given condition. 3) y' = 7 ; y = 20 when x = 1 A) y =…

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Q: Q2. If the solution of the below first order D.E is y = C el(x.y) (x³ + xy²)y = y³ Find the f(x, y).

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Q: Find a particular solution of (20) y′′−3y′−4y=2e−t.

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Q: • 2. Solve by VP: y"' – 3y" + 2y' - et 1+e-x Hint: Answer is y = C1 + €ze* + c3e2x + (e* + 1) -In(e*…

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Q: Q2\ Find the general solution to the given Euler x2y" – 3xy' + 9y = 0

A: Explanation of the solution is given below...

Q: Solve for for the equation y = aln(x + )+ 4tan(;)– 2x O a. T O b. In(4 + x) O c. none of these O d.…

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Q: Show that the solution of T(n)=T(n– 1) +n is 0(n²). Do not

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Q: Find a particular solution to y" + 6y' + 9y = 3z e

A: We use the method of variation of parameters to find the particular solution to the given…

Q: Solve the following equation using Bernoulli D.E. a. Substitution method y = -x²y²cosx 3. +=y

A: The given Bernoulli differential equation is dydx+2xy=-x2y2cos x.....(1) We have to solve the…

Q: Find a particular solution to y″+36y = 60sin(6t).

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Q: If y1=x2+x°is a solution for x²y"-4xy'+6y=0, then the second solution is Select one: a. -In(x+1) O…

A: we have to solve given problem:

Q: 2. xty'= -x³y- csc(xy)

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Q: Suppose that the DE y"" (x) + 7y(x) =70 2³ +123 has a solution of the form y = Az³ + B Find the…

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Q: The general solution of the DE: y = 1 is y = x(x + c) Select one: O True O False

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Q: 4. Assume y(x) : = ea" cosBx is one of the solutions of the DE у3) — Зу" + 7у - 5у —D 0. Then a + B…

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Q: Which of the following is a general solution to the following 4x3y"+4xy'+ (4x²– 25) y=0 O…

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Q: Find the general solution of the DE: y “ – 5y“ + 3y + 9y = 0 יוו -

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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 a particular solution to y′′+36y=60sin(6t) yp=

A: The given differential equation is  To calculate the particular integral let us consider If we put…

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

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Q: Find the general solution or particular solution of each of the following DE 's: 1. (x- 2xy²e*²+…

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Q: 2. Find the general solution of d'y -6 da dr +12 - 8y = 21e2 da

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Q: 1. Find the general solution of 2+ 2xy = 4x y = 2 + Ce* y = 3 - Ce А. С. y = 2 + Ce D. y = 2 - Ce В.

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Q: Find the general solution of the following DE in explicit form. y' = 4+2/y -4x +5

A: To find: The general solution of y'=4+2y-4x+5. Concept used: Power rule of differentiation:…

Q: 5. Find the particular solution of x²y' – 2xy = x* + 3; where y = 2 and x = 1

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

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 general solution of the DE below. y(5) + 5y(4) – 2y“* – 10y“+ y' + 5y = 0

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Q: 2y" — 12" + 4у' + 72у %3D 0

A: Given ode is homogenous. We will find root of this ode then we write solution.

Q: Find the general solution of the following equation valid near the origin: (1+4x2)y"-8y=0 00…

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Q: Find the solution of the D.E whose solution is given as y=2(x^2−1)+ce−x^2

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Q: Find the Solution (1+r?)ds + 21[st²– 3(1+1²)²]dt = 0; when 1 = 0, s = 2. = (1+ s?)13-e-

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Q: 5. Find the particular solution of x²y' – 2xy = x* + 3; where y 2 and x = 1

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Q: B. Find the general solution of each of the following Higher Order LDE with cc y (5) – 9y" = 27

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

Q: 2. Determine the general solution to the equation y' + 2xy = e-2". %3D

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