Graph at least 6 members of each family of solutions. x2+3x+2 3. y' = y2–2

Q: find general solutions (for x>0) of the Euler equation x3y3  -3x2y"+xy'= 0

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Q: Find a solution to the initial value problem, y" + 6x = 0, y(0) = -2, y (0) = -5.

A: y'' +6x=0⇒y'' =-6xIntegrating both sides,⇒y'=-3x2+c1Integrating both sides,⇒y=-x3+c1x+c2 We have…

Q: 11. Find the particular solution of 2ydx = 3xdy, when x -2, y = 1

A: Given : Differential equation :  2ydx = 3xdy And x = -2, y = 1   To find : Particular solution of…

Q: 2. Solve the yk+2+9yk = 4k + cos 3k using method of undetermined coef- ficients.

A: Introduction: All the phrases withinside the connection or equation have the equal traits while we…

Q: Find the singular solution to the Clairaut equation y = xy' + In(- 19 -y').

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Q: find the general solution of the given equation. 3y'' - y' = 0

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Q: x(1-х)у" - Зу' + 2у %3D0

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Q: Solve 1 . Find a particular solution to a' = x – y + e', y = -4x + y +t using undetermined…

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Q: find the solution satisfying the initial conditions: y''-y=x^2 , y(0)=0 , y'(0)=-1

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Q: 4) Find the solution of y'= 2(2xy) passing through (0,1).

A: Given, Equation  y'=2(2x-y) passing through a point (0,1).

Q: Solve the following Euler-Cauchy type equation: 1 (2²D² + 3xD+ 1)y %3D (1 – x)²'

A: The given ODE is given as: x2D2+3xD+1y=11−x2

Q: Find the general solution for the homogenous equation of y′′ − y′ − y = 0.

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Q: Give the general solution of xy²dy = (x³ + y³)dx in explicit form.

A: Given differential equation is  which is homogeneous differential equation.

Q: y" + 2y' = 121?

A: To find the general solution of a given non homogeneous differential equation first we will find…

Q: Use undetermined coefficients to find the particular solution to y'' - y = 4e t Y(t) =

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Q: Find (a) the general solution and (b) the particular solution for the given initial condition. y' =+…

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Q: Solve the two initial value problem y = |y|, y(0) = 1 and y' = y, y(0) = 1 and the graph the two…

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Q: can i get step by step help please

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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: Obtain the family of solutions 1) xydx – (x² +3y² ) dy = 0 2

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Q: If find the value of a. 3 S₁ S² (x + 2y) dydx = 10, 0 a

A: Given: ∫01∫a3(x+2y)dydx

Q: find general solutions (for x>0) of the Euler equation x3y3 +3x2y"+xy'= 0

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Q: 2a) find a solution of y" (x) = y(x) that passes the origin and go trhout the point (In(2),-).

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Q: Find that solution of y’= 2(2x-y) which passes through the point (0,1). Use Linear Equation of Order…

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Q: Find two linearly independent solutions of y" + 3ry = 0 of the form Y1 = 1+ a3x³ + a6x® + · .. Y2 =…

A: We find two linearly independent solutions of the given differential equation  y"+3xy=0.......(1)

Q: a. Find that solution of y' = 2(2x-y) which passes through the point (0, 1). %3D

A: For part a). Given that                      y' = 2(2x-y) =4x-2y                      y' + 2y = 4x…

Q: Find a particular solution to æ' = -x – y + e', y' = 2x + y – ešt using undetermined coefficients.

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

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Q: Suppose we are given y1(x) and y2(x) (with y1 # y2), which are two different solutions of a…

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Q: 5. = y – xy³e-2x у —

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Q: If y and y, are solutions of a non-homogenous equation y" + ay + by =c then y,-Y2 is a solution of…

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Q: (7) Find the general solution to y = (x +y + 1)

A: Given differential equation is: dydx=x+y+1 Let us assume x+y=t 1+dydx=dtdxdydx=dtdx-1…

Q: Solve the Bernoulli Equation xyy' + y² = 2x

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Q: Find the family of solutions of the equation (x2y5 + y3)dx + (x3y4 + x)dy = 0

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Q: The general solution of the DE y"-y" + y'- y=0 is

A: We need to factorize this equation to find the solution.

Q: Find two linearly independent solutions of the equation (x-1)y"+y=O for |x|<1

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Q: Solve the Bernoulli Equation xyy + y² = 2x

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Q: determine by inspection at least two solutions of the given first-order IV . 15. y-  3y2/3, y(0) …

A: Consider the given y'=3y23 and y0=0

Q: Find the solution of (1 + e²)yy = eª that passes through (0, 1).

A: (1+ex)yy'=ex(1+ex)ydydx=exseparation of variablesydy=ex1+exdxIntegrating both…

Q: The general solution of 5uxx – 6uxy +uyy = 0 -

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Q: Find the particular solution of: y' – 4y = x²e* that satisfies y(0) = 2.

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Q: Use undetermined coefficients to find the particular solution to y'' + y' – 3y = 4t + 5 Yp(t) = %3D

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Q: Find the equation of a line parallel to x = -8+ 2y that passes through the point (8, –2). Oy = -x –…

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Q: The general solution of the DE y" -y" + y'-y 0 is

A: we have to find out the general solution of the differencial equation y'''-y''+y'-1=0

Q: S'z xdx (1+x)*

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Q: a. Find that solution of y' = 2(2x-y) which passes through the point (0, 1).

A: SINCE YOU HAVE ASK MULTIPAL QUESTION, SO WE WILL ANSWRING ONLY FIRST QUESTION.

Q: Find (a) the general solution and (b) the particular solution for the given initial condition. 8 y'…

A: Given Data: Differential Equation: y'=8x+6x4-2x6 ......1 Initial condition: y1=8

Q: 1 Solve 1 3D7 for z. y. 1-

A: 1x-1y-1z=7

Q: Find a solution to the initial value problem, y" + 18x = 0, y(0) = -4, y'(0) = –5. %3D

A: To Determine: Find the solution to the initial value problem.

Q: Find the general solution of y"+25y=sec(5x)

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