Find the general solution of the given equation y" + y = 0

Q: (f) y" + 6y' + 9y = 0

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Q: ) Solve the initial-value problem dy :-2y 2x* ;y(2) = 8 %3D x- dx

A: We have to solve the given differential equation using the initial condition. Rearranging the…

Q: dy = 2x- 7, y(2) = 0. dx

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Q: Given the initial condition y(0) = 1, find the particular solution of the equation yy' - 6x = 0

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Q: Solve the Bernoulli equation y' + xy = y4.

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Q: Find the solution satisfying the initial conditions: y" - y = x2 y(0) = 0 y'(0) = -1

A: Given that: y''-y=x2

Q: Solve the initial value problem and find y(1): y y' = xe -4", y(0) = - |

A: Here given as Integrating both sides Substitute y2=u thus 2ydy=du

Q: Find the solution to the initial value problem y'=x²-, y(2) = 3.

A: Solution of the initial value problem

Q: In Bernoulli equation y' - xy = xy³, the value of 1(x) is ex²

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Q: Find a particular solution to the differential equation y" + 3y' + 2y = -8t³. Yp

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Q: Given the initial condition y(0) = 1, find the particular solution of the equation y' = e3x - 2y

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Q: Solve, explicitly for y, the initial value problem: e@y (21x – sec(x)); y (0) = 180

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Q: Find the general solution to the equation xy” + 2y'− xy = 0 Using Frobenius.

A: xy''+2y'-xy=0 →l  Let y=∑n=0∞ cn xn+r  ⇒y''=∑n=0∞ cn(n+r)xn+r-1   ⇒y''=∑n=0∞ cn(n+r)(n+r -1)…

Q: Find the solution of the initial-value problem dy - 2y = 2.x", y(2) = 8. dx

A: Convert this IVP into linear differential equation by dividing by x then proceed to fund Integrating…

Q: 5. Find the solution of the different ial equation, = xe", that satisfies the initial condition y(0)…

A: Given differential equation is  dydx=xey, y0=0

Q: initial-value

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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: dy - y = xy2 dx

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Q: Find the solution to the initial-value problem. = y3xe*, y(0) = 1 dx .2 -2

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Q: solve the solution of the Bernoulli's equation 3yły' + - 8(x + 1) = 0; y(0) = 0 x+1

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Q: the differential equation 3(3x^2 + y^2)dx - 2xydy = 0 is homogeneous of what degree?

A: The given homogeneous differential equation is 33x2+y2dx-2xydy=0.

Q: Find the differential equation having the solution as: a. y = C,e¬x + C2e¬2x + x b. y = C, + C2e³x

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Q: Solve the Bernoulli equation dy *+y = xy

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

A: To find general solution of differential equation 2y+x+1y'=3x+3

Q: Find the general solution of the given Attached equation

A: Differential eq:9d2ydx2+6dydx+y=0The auxiliary eq is 9m2+6m+1=0

Q: 3. Solve y' = , with initial condition y(1) = 0. y2 – 1 x3

A: It is given that the differential equation dydx=y2-1x3. Using variable and separable method to…

Q: Find the general solution for the differential equation. y' = 2 - x³ + x6

A: Given query is to find the solution of the differential equation.

Q: (e) y" – 4y' + 4y = 2x

A: To find the general solution

Q: solve using the Initial Value Problem.  xy' + y = ex ,       y(1) = 3

A: Given,

Q: Find the general solution of the differential equation. y′ + √x y = 9√x

A: To find the general solution of the differential equation y'+xy=9x

Q: Solve the initial value problem y" + y' – by = 0, y(0) = 0, y'(0) = 5

A: Topic: differential equation

Q: Find a particular solution to the differential equation Ур || y" + 5y' + 6y=-108t³.

A: Given differential equation is y''+5y'+6y=-108t3 We have to find a particular solution for it.

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

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Q: Find the value of y (0.4) if y' + 0.2y = 0, y(0) = 5. Solve analytically.

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Q: Find the differential equation having each equation as general solution. 7.) y= x + C,x + C,e 11.)…

A: An ordinary differential equation is an equation containing independent variables, dependent…

Q: Find general solutions of the differential equation  9x^2y^2+x^(3/2)y'=y^2

A: Given differential equation: 9x2y2+x32y'=y2

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

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

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Q: Find the general solution of the differential equation. у" - 400у %3D0 ... y(x) =

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Q: Find the solution of the initial condition problem: ÿ +t°ÿ+3t?y = 0, ,y(0) = 1, ġ (0) = -1.

A: To solve the given differential equation with given initial conditions: y¨+t3y˙+3t2y=0;y0=0,y˙0=−1

Q: Specifically a differential equations problem. Question in pic below.

A: We are given the differential equation,                                   First, we will solve the…

Q: Find the general solution of the differential equation. 11x y' = y

A: We have to find the general solution of the given differential equation.  For this we will…

Q: x2-y2 dx Зху

A:

Q: Find the general solution of the differential equation -y" + y = 3e4 – 2

A: Given: Second order differential equation -y''+y=3e2t-2 ........... * To find: General solution of…

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: Solve each of the equations. Integrating Factors (y² – x y) dx + (2x² – xy) dy = 0; y (1) = 1

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Q: Solve the equation (4y+2x– 5)dx + (6y +4x– 1)dy = 0 subject to the initial condition y(-1)= 2.

A: Consider a first order linear homogenous differential equation of the form, Pdx+Qdy=0→1 where P=fx,y…

Q: с. у -у%3х y = x

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

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.