A particular solution of x²y" - 2y = 3x²-1, t>0, y₁(x)=x², v₂(x)=x-¹

Q: Q3/ Solve the following equations: 1- х(2у — 3)dx + (x2 + 1)dy %3D0 dy 2- dx 4y x (у-3) 3. y' = 2xy…

A: Note that there are so many ways to write the final answer of the differential equation.

Q: If y = Vx? – 2x then y' 2(x-1) 3x2-2x %3D

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Q: Find the general solution of x(x + 3)dy = 2dy + √(9- y²)(12x + 9 + 4x²) dx.

A: We will separate variables and then will integrate it to find general solution of given differential…

Q: find the seril solution of the equation y``+  4xy = 0  at the point  x0 = 0

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Q: Obtain two linearly independent solutions valid near x = 0 x2y" + x(x-1)y' + (1-x)y = 0

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Q: Given the Bernoulli's equation Dy/DX+yP(x)=y^n Q(x) and x=y^1-n, reduce the equation to the linear…

A: Given differential equation is                                           dydx+yP(x)=ynQ(x);  x=y1-n…

Q: p" +2y' – xy = 0 n(x)= e

A: Given

Q: 5. [10 points] Find the general solution y"-6y' +9y = x*e*

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Q: What physical systems might the Chini equation, y*y' + f(x) = g(x)*y, represent? Can you tell me…

A: The Chini equation, given by  y∗y′+f(x)=g(x)∗y , appears in various physical and engineering…

Q: Find the general solution of the D.E (y^2 – 2xy + 6x)dx – (x^2 – 2xy + 2)dy = 0 Show your solutions…

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Q: Put the equation into the form x'(t) = g(t)h(x), and solve by the method of separation of variables.…

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Q: У). y), where

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Q: Solve the IVP: X' = AX, where -2 1 A = -5 0 3 -2 and -2 X(0) = -1 2

A: To find the solution of X'=AX where, A=−210−50003−2X0=−2−12

Q: Verify that the function y = c1e (-k+2t)x + c2e (-k-2t)x is a solution to y " + 2ky'+ (k 2 + 4)y =…

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Q: Find the general solution of the equation

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Q: Find the GS of 2 (x - α)² = where a is an arbitrary constant and you may want to consider "pilot" y₁…

A: As per the question we are given the following nonlinear first order differential equation…

Q: 7 0-3 -9 -2 3 18 0-8 y, y(0) = 2 3

A: Given y'=70-3-9-23180-8y Also given y0=23-1   To reduce to row echelon form and solve for constant…

Q: 5. Given: f (x) = ax³ – 9x² + 2x – 4 and g(x) = bx³ – 5x² + 62x + 70 | Solve for all values of a and…

A: We have to find

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: xy" + xy² + 4y = /Nx Find the solution y(x)

A: We will find the solution of the differential equations.

Q: can you explain if this is true or false if y=x2+y2, then y'= 2x+2y

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Q: [v= -y +2x ,x' = 4y + x + t

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Q: If u(x) = x3, then du = 3x2.

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Q: (x³-4x+1)vx++5x+5 find y' 4x2+5x

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Q: Solve for the general solution * (4xy+3y – x) dx + x (x + 2y) dy = 0 x' (4xy² + 4y – x) = c x²…

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Q: 2x2y'' + 3xy' - y = 0 , x>0   y1(x)= x1/2 and y2(x)=x-1 Please verify that I have solution.

A: Differential equation.

Q: (2) x (x+3)y"+2y'+y=0 solve for yox)

A: To solve the differential equation: x(x+3)y''+2y'+y=0 We can start by assuming a solution of the…

Q: Find a general solution of y"=(-2+2isqrt(3))y

A: Given that, the differential equation is- y''=-2+2i3y On simplifying, y''--2+2i3y=0

Q: If y= (x³ + 1)* , then y' = ? A) None of the given choices В 6x²(x³ + 1) O (3x2)2 D D 2(3x²+1) E…

A: Given:- y = (x3+1)2 To find:- y'