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by: Breana Kuhn

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3

# Macroeconomics I ECON 810

Marketplace > Kansas > Economcs > ECON 810 > Macroeconomics I
Breana Kuhn
KU
GPA 3.77

Shu Wu

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COURSE
PROF.
Shu Wu
TYPE
Class Notes
PAGES
3
WORDS
KARMA
25 ?

## Popular in Economcs

This 3 page Class Notes was uploaded by Breana Kuhn on Monday September 7, 2015. The Class Notes belongs to ECON 810 at Kansas taught by Shu Wu in Fall. Since its upload, it has received 36 views. For similar materials see /class/182467/econ-810-kansas in Economcs at Kansas.

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Date Created: 09/07/15
Econ 810 Macroeconomics l Handout on Differential Equations Shu Wu February 37 2009 1 Linear Differential Equation with Constant Co ef cients The general form of the linear rst order ODE with constant coef cients is W am W 0 Solution W am W W ago 76 dle ytl 7 at T 7 75 Mt Hence sagif 7 y0 70 ea9xsds or yt 75quot 0t ea9xsds l fag0 We need boundary conditions to pin down the constant Example the inter temporal budget constraint Assume that the interest rate is constant T the instantaneous budget constraint is dt rat wt 7 C75 7 nat wt r 7 nat 7 C75 The boundary conditions are a0 is given7 and limtH00 ate 7 t O Solve the differential equation dt 7 r 7 nat wt 7 C75 d6 lt gt at Tie lt gtltwlttgt7clttgtgt atelt gtt 7 am 7 5quot gt5ltwltsgt 7 cltsgtgtds or t t 103570770 eiltringtscsds 10 5777 5wsds 0 0 Now let t 7 007 we have 00 5 r7ntctdt am 00 57r7ntwtdt 0 0 2 Linear Differential Equation with variable Coef cients W atyt W 0 Solution De ne w 5 asds Hence t 5alttgttyt Mo 7 0 ea99msds or t yt 757att eas5msds e atty0 0 Again we need boundary conditions to pin down

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