Use the initial condition to find the particular solution of the differential equation. Differential Equation x(y + 2) + y' = 0 Initial Condition y = -8 when x = 0

Q: (;+-) dx + (ve» +) dy = = 0 x2 + y2, x2 + y2.

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Q: 3. For the below ordinary differential equation with initial conditions, state the order and…

A: Given differential equation x2y2-3dydx=12y  y(1)=2. The objective is to solve the differential…

Q: Solution of differential equation xy' - y = 0 (y' = dy/dx) is...

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Q: Use separation of variables to find the general solution of the differential equation. x2 + 6yOy = 0…

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

Q: Determine whether the equation is exact. If it is exact, find the solution. If the differential…

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Q: Solve the differential equation by variation of parameters, subject to the initial conditions y(0) -…

A: It is given that the differential equation is 2y''+y'-y=x+5 The auxiliary equation is 2r2+r-1=0…

Q: 3. Find the general solution y = Yc + Yp to the differential equation. Use the uppercase letters C…

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Q: 4. x"+4x' +4x =0.

A: Let, x = emt be a trial solution. So, x' = memt  &, x" = m²emt So, the characteristic equation…

Q: Solve the differential equation with appropriate method. Express final answer free of fractions and…

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Q: 6. Given a differential equation with coefficients linear in two variables. If the DE represents…

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Q: 2. (x- 3y + 3)dx + (3x + y + 9)dy = 0

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Q: Consider the differential equation: 1 y" – y = What is the general solution?

A: We have to find the general solution of the given problem.

Q: Solve the differential equation x y' = In x-3xy with initial-value y(1) =2.

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Q: Solve the differential equation by using appropriate method or substitutions. dy/dx = 2 +…

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Q: the differential. Equation by eliminating the arbitrary constant  y = Ae2x + Be-2x

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Q: Find the explicit particular solution of the differential equation for the initial value provided. -…

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Q: Solve the differential equation by variation of parameters, subject to the initial conditions y(0) =…

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Q: Use the initial condition to find the particular solution of the differential equation. Differential…

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Q: One solution of the differential equation y''+y'=0 is y=e^-x. A second linearly independent solution…

A: We will find out the required solution.

Q: (D² - 1)y= 2 1+ex

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Q: Find the solution of the differential equation y'=xey-x^2 when y(0)=0.

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Q: Use the initial condition to find the particular solution of the differential equation. Differential…

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Q: Given the differential equation -(승) (중), y" Find two values of r such that y = x' is a solution of…

A: The given differential equation is y''-6xy'-8x2y=0. Let y=xr. This gives  y'=rxr-1     and…

Q: Find the general solution and the particular solution of differential equation given by the initial…

A: To find the general and the particular solution of the given differential equation.

Q: y' + y = y²e*

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Q: Solve the differential equation with appropriate method. Finalize answer in terms of x and C…

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Q: Determine the solution to the initial value differential equation y'+ 3 y = 4 x y(0) = 3 y (x)=

A: First order differential equation : Consider the first order differential equations…

Q: y" - y = e2* - sin x

A: The given question has been solved in detail

Q: Solution of given differential equation at x = 2 is (1 – a²) – 2æy = x² - (Assume zero initial…

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Q: Find the general solution for differential equation. Verify that  solution satisfies the original…

A: Consider the given differential equation dydx=8x2y-9xy and rewrite it in the form of a separable…

Q: Find the particular solution of the differential equation that satisfies the initial condition.…

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Q: y" – y' = 2 sint.

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Q: Use the initial condition to find the particular solution of the differential equation. Differential…

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Q: Using the method of undetermined coefficients, find the general solution to the differential…

A: The given differential equation is y′″ - 3y″ - y = 4et                                    ...... (1)

Q: = 2x (y(0) = 4

A: Given: y2y'=2xy(0)=4

Q: (D² - D-2)y = cos x

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: y" -y'-zy= 4et

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Q: Determine whether the equation is exact. If it is exact, find the solution. If the differential…

A: A differential equation M(x,y)dx+N(x,y)dy=0 is said to be exact iff ∂M∂y=∂N∂x

Q: Use substitution to find a general solution of the differential equation  a)  x^3*y'+x^2*y=y^2…

A: We need to convert Bernoulli equation into linear differential equation form by using substitution

Q: x*y'(x) + (1+x) * y(x) - 2 = 0 Find the general solution of the differential equation. Since y(1)=…

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Q: Solve the differential equation and initial condition and verify that your answer satisfies both the…

A: Given,           y'=2xy2           y0=13

Q: Solve the differential equation = 4x+3y by using the substitution u = Ax+ By+C. The resulting…

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Q: Solve the differential equation for y= y(x) if y+2ry + 2x = 2 + 2y given the initial condition that

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Q: For the differential equation y" --y' --= 0, find a particular solution which satisfies the initial…

A: To find the particular solution for the given differential equation which satisfies the initial…

Q: Use the initial condition to find the particular solution of the differential equation. Differential…

A: topic - differential equations

Q: solve the differential equation using the substitution method. (3siny-5x)dx+2x2cotydy=0

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Q: 30. x" + 10x =0.

A: We have to find General Solution of the given Differential equation.

Q: y'-5y= x'e* – xe* ito

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Q: Solve the differential equation by variation of parameters, subject to the initial conditions…

A: The given differential equation is 2y"+y'-y = x+5 with the initial condition y0=1, y'0=0 To solve…

Q: -2у y+2xyy' = e" y 'y'

A: Please see the answer in step 2

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.