## Related questions with answers

Find a differential equation whose general solution is y=c1e−t/2+c2e−2t.

Solutions

VerifiedWe need to find a differential equation whose characteristic equation has roots $\frac{-1}{2}$ and -2. One such equation is

$(r+\frac{1}{2})(r+2) = r^2+\frac{5}{2}r+1=0.$

Multiplying both sides by 2 we get an equation without fractions,

$2r^2+5r+2=0.$

The corresponding differential equation is

$2y''+5y'+2y=0 .$

We need to find a differential equation whose characteristic equation has roots $-\frac{1}{2}$ and $-2$. One such equation is

$\begin{equation*} (r + \frac{1}{2})(r + 2) = r^2 + \frac{5}{2} r + 1= 0 \end{equation*}$

We can multiply both sides by $2$ to get rid of the fraction,

$\begin{equation*} 2r^2 + 5r + 2 = 0 \end{equation*}$

The corresponding differential equation with this characteristic polynomial is

$\begin{equation*} 2y^{\prime\prime} + 5y^\prime + 2 = 0 \end{equation*}$

## Create an account to view solutions

## Create an account to view solutions

## Recommended textbook solutions

#### Elementary Differential Equations and Boundary Value Problems

10th Edition•ISBN: 9780470458310 (7 more)Richard C. Diprima, William E. Boyce#### A First Course in Differential Equations with Modeling Applications

10th Edition•ISBN: 9781111827052 (2 more)Dennis G. Zill#### Elementary Differential Equations and Boundary Value Problems

11th Edition•ISBN: 9781119320630Douglas B. Meade, Richard C. Diprima, William E. Boyce#### Differential Equations with Boundary-Value Problems

9th Edition•ISBN: 9781305965799Dennis G. Zill## More related questions

- differential equations
- differential equations
- differential equations

1/4

- differential equations
- differential equations
- differential equations

1/7