Solve the differential equation with constant coefficients

Fatima Hasan · Nov 23, 2018

Homework Statement

Printed text reading 'Solve the DE:' above the equation 2y'' - 2y' + 7y = 0.

Homework Equations

The Attempt at a Solution

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Handwritten-style typeset working for a second-order linear ODE: 2y'' - 2y' + 7y = 0, auxiliary equation 2λ² - 2λ + 7 = 0, roots λ = (2 ± √(4-56))/4 = 1/2 ± √(56)i, and general solution y(x) = C1 exp(x/2)cos(√(56)x) + C2 exp(x/2)sin(√(56)x).

Is my answer correct?

mjc123 · Nov 23, 2018

How do you get √56? Shouldn't it be (√52)/4 = (√13)/2?

Fatima Hasan · Nov 23, 2018

mjc123 said:

How do you get √56? Shouldn't it be (√52)/4 = (√13)/2?

Worked solution of a second-order linear ODE: characteristic equation 2λ² - 2λ + 7 = 0, roots λ = 1/2 ± i√13/2, and general solution y(x) = C1 exp(x/2) cos(√13x/2) + C2 exp(x/2) sin(√13x/2).

Is it correct now ?

mjc123 · Nov 23, 2018

Looks OK to me.

Mark44 · Nov 23, 2018

Fatima Hasan said:

View attachment 234491
Is it correct now ?

1. In the future, please post questions about differential equations in the Calculus & Beyond section. I will move the ones you have posted in the Precalc section.
2. You don't need to ask us to check your work for these kinds of problems. Just substitute your solution in the original diff. equation.

Solve the differential equation with constant coefficients

Homework Statement

Homework Equations

The Attempt at a Solution

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