Explain Properties of the Solutions of y''+y=0 ?

Q: 3 (3x? — 6ху) dx — (3x? + 2у) dy 3D0 -

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Q: y' + 3xeY = 0

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Q: y'= (x²y- y)/(y+1);when x = 3, y = -1

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Q: y + 3xy' – 2(y')³ = 0

A: Product rule of differentiation: (fg)'=fg'+gf' Chain rule of differentiation:…

Q: y" – 2y' + y = ex x5 when y(0)=1; y'(0)=2

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Q: x² + y? = r2 O y = - y' = - y

A: topic - differential equation

Q: y" +9y' = 9 tan 3x

A: The solution is given by using method of variation of parameters as follows

Q: 3. Determine a homogeneous linear equation with real, constant coefficients that is satisfied by: y…

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Q: Solve by applying "Differential Equation using Substitution Suggested by the Equation" (2x + y)dx–…

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Q: Find general solutions of the differential equation  2xyy'=x^2+2y^2

A: To solve:

Q: What can be the method of solving the DE? 2xyy' = y² – 2x³3 Bernoulli's DE Substitution suggested by…

A: Let's find which method is suitable.

Q: Find general solutions of the differential equation  (2x+1)y'+y=(2x+1)^3/2

A: Consider the differential equation:

Q: equation

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Q: Obtain the differential equations satisfied by the given puiiicular 3. y = e5x - 3x - x2 4. y = e3x…

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

Q: SHOW THAT THE DIFFERENTIAL EQUATION IS LINEAR EQUATION OF ORDER ONE 2. (y – 2)dx + (3x – y) dy =&

A: We can solve this problem as follows:

Q: y"″ − 3y" − 4y' + 12y = 0 -

A: To find the general solution of the differential equation y'''-3y''-4y'+12y=0

Q: Find the approximate height of the curve y = x3 – 2x2 + 7 at the point where x = 2.98. (SOLVE BY…

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Q: Solve the differential cquation d'y by using the method of variation of parameters.

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Q: y' = (x+y– 2)² (х-у)?

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Q: What is the general solution of the differential equation 2xyy' y? - 2x³ ?

A: We have to find the general solution of the given differential equation 2xyy'=y2-2x3 .

Q: Find general solutions of the differential equation      2x^2y-x^3y'=y^3

A: 2x2y-x3y'=y3 We need to find the general solutions of the differential equation.

Q: Solve the differential equation 2xyy' = 1 + y". If y = 3 when x = 2, determine y when x = 1.

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Q: 4.x+xy? y-x²y ,2 dy dx

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Q: Find x for which the line tangent to the parabola y = 4x – x2 is horizontal.

A: In this question, we need to find the value of x at which the tangent line is horizontal.

Q: Find the general solution of the differential z-y+3 equation y' I-y

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Q: 3. y"-3y" +3y'-y=x-4e*

A: y'''-3y''+3y'-y=x-4ex for the homogeneous system, the auxiliary equation is  r3-3r2+3r-1=0 r-13=0…

Q: Find a differential equation whose general solution is y = c₁et + c₂e-4t . = 0

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Q: ()y -= 0 (3y²-x²* 2y4

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Q: (sin² y + x coty)y' = 1

A: I have appended the formula used in the solution part of the question.

Q: Find the particular solution of the curve which passes through the point (1,2) if the equation of…

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Q: Find the general solution of the inhomogeneous equation y" + 3y' = te'.

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Q: give an own differential equation     solve for the solution when  x=2 and y=0

A: Given, We have to write own differential equation  and Write the particular solution when x = 2  and…

Q: 6. Show that 2y2 dy x² + y2 dx is homogenous equations. Hence, solve the equation.

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Q: Find general solutions of the differential equation    (x+2y)y'=y

A: Given differential equation is Convert it in linear differential equation by simplifying. This is…

Q: What are the order and degree of the differential equation representing the family of parabolas y2 =…

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Q: /y' + 10 = 0, y(0) = 2 and y'(0) = 4 %3D %3D

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Q: Find a differential equation whose general solution is y = ciet + cze-4t. %3D

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Q: solve the equation using differential equation linear in x and y: (2x-3y-5)dx + (3x-y-2)dy = 0;…

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Q: 6.) y' + (4/x) y- (x')ly) =0

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Q: Find the equation of the line tangent to y = x2 – 3x – 5 and parallel to the line y = 3x – 2.…

A: Explanation of the answer is as follows

Q: x³y" + 3x?y" = 2x +1

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Q: Find the differential equation of the parabolas with vertex on the x-axis and axis of symmetry is…

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Q: Use the method of variation of parameters to find & particular solution of y" – 2y + y = and write…

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Q: Verify that the general solution satisfies the differential equation. Then find the particular…

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Q: 2. xy' - y = y cos 3x

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Q: Determine the differential equation whose general equation is 1. y = Ce-2x + C,e3x 2. y = Ce* +…

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Q: Solve the differential equation by variation of parameters 16x у" - 16у y(x) =

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Q: Use inspection to find four solutions to the differential equation: (y')^2+y^2=1

A: The given differential equation is

Q: Find a differential equation whose general solution is 6t y = c₁et + c₂e -3t = 0

A: We find a differential equation whose general solution is y=c1e6t+c2e-3t.

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.