## Related questions with answers

Question

Solve the IVP. Check that your answer satisfies the ODE as well as the initial conditions. Show the details of your work. y''+y'-6y=0, y(0)=10, y'(0)=0

Solution

Verified3.4 (7 ratings)

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Step 1

1 of 4We have

$y''+y'-6y=0$

The characteristic equation,

$\begin{gather*} \lambda^{2} + \lambda - 6 = 0 \\ \text{its roots:} \quad \lambda_{1} = 2 \quad \text{and} \quad \lambda_{2} = -3 \end{gather*}$

where we see that we have a case of two distinct real roots, which means that the general solution of this Second-Order Linear ODE would be of the form

$\mathbf{y=C_{1}e^{\lambda_{1} x} + C_{2}e^{\lambda_{2} x}}$

Therefore,

$y=C_{1}e^{2x} + C_{2}e^{-3x}$

and

$y'=2C_{1}e^{2x} -3C_{2}e^{-3x}$

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