{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

practice2(3)

# practice2(3) - Practice Exam 2 MAP 2302 1 Solve the...

This preview shows pages 1–2. Sign up to view the full content.

Practice Exam 2: MAP 2302 1. Solve the following IVP: y ′′ + 5 y + 4 y = 0 , y (0) = 1 , y (0) = 0 Answer: 4 3 e t 1 3 e 4 t 2. Given is an RC-circuit with R = 1 (Ohm) and C = 0 . 5 (Farad), driven by a generator that delivers E ( t ) = sin t (Volts). Suppose that the initial voltage over the capacitor is 1 Volt. Determine the voltage v C ( t ) over the capacitor. Answer: v C ( t ) = 22 5 e 2 t + 4 5 (sin( t ) cos( t ) 2 ) 3. What is the structure of the particular solution to: y ′′ + 2 y + 2 y = ( t 2 + 1) e t cos( t ) Answer: t ( A 2 t 2 + A 1 t + A 0 ) e t cos( t ) + t ( B 2 t 2 + B 1 t + B 0 ) e t sin( t ) y ′′ 4 y + 4 y = ( t + 3) e 2 t + sin( t ) + t e t Answer: t 2 ( A 1 t + A 0 ) e 2 t + B 1 cos( t ) + B 2 sin( t ) + ( C 1 t + C 0 ) e t 4. Find the general solution on the interval ( π/ 6 ,π/ 6) of y ′′ + 9 y = tan(3 t ) Answer: v 1 ( t ) y 1 ( t ) + v 2 ( t ) y 2 ( t ) , where y 1 ( t ) = cos(3 t ) , y

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

practice2(3) - Practice Exam 2 MAP 2302 1 Solve the...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online