Give a particular solution for y"– 2y' + y = ; ex 1+x2

Q: 4. Find the particular solution of y(x² + y²)dx + x(3x² – 5y²)dy ;where x = 2 and y = 1. -

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Q: x'y" – xy' = Inx

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Q: Show that ¢(x) = Ce³* + 1 is a solution to dy/dx – 3y = -3 for any choice of the constant C. Thus,…

A: We have to check Q(x)=Ce3x+1 is solution of given differential equation.

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

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Q: he Bernoulli equation for y by making 4y + y³. - following initial condition: u(0)

A: Introduction: A differential equation is a mathematical expression that contains the derivative of…

Q: dx 5x cos(3t) dt with x(0) = -4.

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

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Q: Find all singular points for the differential equation (x+4 x)y" + sin(x) y' –x² y=0

A: Given differential equation is  x3+4xy''+sinxy'-x2y=0y''+sinxx3+4xy'=x2yx3+4x Let P=sinxx3+4x  ,…

Q: fx' = 9x + 7y ly' = 2x + 2y

A: We see that x'y'=9722xy. 9722The eigenvalues of A are the roots of the characteristic equation…

Q: 2. Find the particular solution to y " = sin(x) given the general solution y = -sin(x) + Ax + B and…

A: The general solution to the differential equation y''=sinx is y=-sinx+Ax+B

Q: 4. Find the General and Particular solution of dy -8 sin 4x ; y = 6 when x = 0 dx dy

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Q: x²(a+x) 2. Family of strophoids with the equation y² %3D a-x

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Q: 2. Find the particular solution of sin y(x+sin y) dx +2x² cos ydy = 0 :3(-1) = 2

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Q: The differential equation of the family of curves orthogonal to x² + y? = C² is

A: Solve the above questions.

Q: If we use the method of variation of parameters, the particular solution of the following…

A: We have to assume the particular solution first.

Q: 3. Find the general solution of differential eguation y" - v' - 6y = 0

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Q: Find the solution of the equation yy' = x ex-y with initial condition y (0) = 0. Is it possible that…

A: A differential equation is an equation that involves derivatives or differential coefficients or…

Q: 1. Find the general solution (5x*y – sin (x))dx +(2x°y-cos (y))dy = 0

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Q: 11.Solve dy - x+) y(2) = 2 by Fourth order Runge-Kutta Method at x = 2.5, and x = 3 %3D dx

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Q: Find the largest interval in which the solution of the initial value problem y" + csc(t) y' +…

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Q: 1. If y"+y= 2x + 3e* then the roots of equation, r₁=. 12 = lyp= = second order differential equ and…

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Q: 4. Obtain the particular solution of (D² + 4) y = sin x + sin 2x

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Q: The actual solution to the differential equation y = 7 with the boundary condition y(0) = 8 is O y =…

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Q: Solve the initial value problem: cos z – 3x?y – 2æ) dx + (2y sin x – x° + In y) dy = 0; y (0) - -- -…

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Q: Obtain the roots and the factored operator form linear differential equations y = x2 – 5 sin 3x y =…

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

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Q: (f) y' – 2y = 1 + 2x – sin(x)

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Q: Show that y is a solution of differential equation = 1-. dy %3D dx

A: y'(x)=1-yx We can simplify it as: dydx+yx=1First-order linear ordinary differential equation.…

Q: The differential equation obtained by eliminating the arbitrary constants A and B from the relation…

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Q: 2. Find the particular solution of (3sin y- 5x) dx+2x cot ydy = 0 ;y(-1)=-

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Q: By using variation of parameters, what is a possible value for u'1 for the differential equation y''…

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Q: Suppose that x = 0 is a regular singular point of the differential equation x²y" – x(x + 3)y' + (x +…

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Q: Show that the function y=ex(sin2x+cos2x) is a solution of the differential equationy′′−2y′+5y=0.

A: We find the first two derivatives of y using the product rule

Q: 6. Given that y = 0 when x = 1, show that the solution of the differential dy equation 2xy- - = y² +…

A: Answer and explanation is given below....

Q: 4) Let y(x) be the solution of the initial -value problem y' = cos(x + y), y(0) = 0. Use Euler's…

A: To find the solution of initial value problem.

Q: Find the particular solution that satisfies the initial condition. y' +y=6e*; Initial Condition: y=3…

A: we camparing the given equation with dy/dx+py=Q  and solve it . see 2nd step.

Q: 5. Find the General and Particular solution of 2 = 3y ; y = 3, when x = 0 dy dx

A: We have dydx=3y Now, we can write this as: dyy=3dx Now, integrate both sides: ∫dyy=∫3dx⇒lny=3x+C…

Q: The Integrating Factor of the differential equation dy dr y = 14x? is x-14 25 e5z

A: The given differential equation is,  dydx-5xy=14x2To find its integrating factor.

Q: 4. Find a particular solution of y" + y' = cost cos 2t cos 3t.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

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

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Q: The differential equation 3y(x -1dx+(x³ +8y– 3xdy = 0; is exact because OM ON %3D

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Q: Find the terminal value, lim y (r), for the solution of differential equation dy + 3z'y - 6z". dr

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Q: solve the Initial Value Problem using Separation of Variables. y' = cos2x, y(0) = π/4

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Q: x dy + y dx = 3x²y² dx, y(-1) = 2

A: Rewriting given differential equation into standard form of bernoulli equation

Q: The differential equation (3ycosx+ 4xe* + 2x²e* ]dx + 3(sin x + 1 )dy = 0 is exact because ƏM ƏN

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Q: dy 2. dx 2y = x°y?

A: Using method of Bernoulli Differential equation.

Q: Find the particular solution of the differential equation (2xy - sin x)dx + (x² - cos y)dy = 0, when…

A: Exact differential equations

Q: The differential equation (2x' - xy - 2y+3 dx- (x²y+2xdy = 0 is exact because OM ON

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Q: Consider the differential equation (10x³y* + e=y + 3 sin(4x + 3y))y' + (6x²y5 + 4 sin(4x + 3y) + 2)…

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