Consider the differential equation y '' − 2y ' + 10y = 0; ex cos(3x), ex sin(3x),...

Consider the differential equation y '' − 2y ' + 10y = 0; e^x cos(3x), e^x sin(3x), (−∞, ∞).

Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval.

The functions satisfy the differential equation and are linearly independent since W(e^x cos(3x), e^x sin(3x)) = _____ANSWER HERE______ ≠ 0 for −∞ < x < ∞.

Form the general solution.

y = ____ANSWER HERE_____

Expert Solution

Colby Messinger answered 1 year ago

Solve the differential equation by variation of parameters. y'' + 3y' + 2y = cos(ex) y(x)...

Solve the differential equation by variation of parameters. y'' + 3y' + 2y = cos(ex) y(x) = _____.

Solve the Differential equation y'' - 2y' + y = ex

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given the 3rd order differential equation: y''' - 3y'' + 2y' = ex / (1 +...

given the 3rd order differential equation: y''' - 3y'' + 2y' = ex / (1 + e-x) i) set u = y' to reduce the order of the equation to order 2 ii) solve the reduced equation using variation of parameters iii) find the solution of the original differential equation

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Determine the solutions for y = y(x) for the differential equation cos x − x sin x + y 2 + 2 x y dy/dx= 0.

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y''' + 2y'' − y' − 2y = sin(4t), y(0) = 0, y'(0) = 0, y''(0) = 1

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Solve the differential equation y'' − y' − 2y = 9e^2t , with initial conditions y(0) = 3, y' (0) = −2, using two different methods. Indicate clearly which methods you are using. First method: Second method:

Consider the parametric equation of a curve: x=cos(t), y= 1- sin(t), 0 ≤ t ≤ π...

Consider the parametric equation of a curve: x=cos(t), y= 1- sin(t), 0 ≤ t ≤ π Part (a): Find the Cartesian equation of the curve by eliminating the parameter. Also, graph the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases. Label any x and y intercepts. Part(b): Find the point (x,y) on the curve with tangent slope 1 and write the equation of the tangent line.

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