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An electric circuit contains a 1-H inductor, a 4-92 resistor, and a voltage source of cost. The resulting differential equation relating the current i and the time t is di/dt + 4i= cos t. Find i after 0.5 s by Euler's method with At = 0.1 s if the initial current is zero. Solve the equation exactly and compare the values.

An electric circuit contains a 1-H inductor, a 4-92 resistor, and a voltage source of cost. The resulting differential equation relating the current i and the time t is di/dt + 4i= cos t. Find i after 0.5 s by Euler's method with At = 0.1 s if the initial current is zero. Solve the equation exactly and compare the values.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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An electric circuit contains a 1-H inductor, a 4-9 resistor, and a voltage source of cost. The resulting differential equation relating the current i and the time t is di/dt + 4i= cos t. Find i after 0.5 s by Euler's method with At = 0.1 s if the initial current is zero. Solve the equation exactly and compare the values. Use Euler's method to find i after 0.5 s. = 0.2192 A approx (Round the final answer to four decimal places as needed. Round all intermediate values to nine decimal places as needed.) Solve the equation exactly to find i after 0.5 s. exact = A (Round to four decimal places as needed.)
Transcribed Image Text:An electric circuit contains a 1-H inductor, a 4-9 resistor, and a voltage source of cost. The resulting differential equation relating the current i and the time t is di/dt + 4i= cos t. Find i after 0.5 s by Euler's method with At = 0.1 s if the initial current is zero. Solve the equation exactly and compare the values. Use Euler's method to find i after 0.5 s. = 0.2192 A approx (Round the final answer to four decimal places as needed. Round all intermediate values to nine decimal places as needed.) Solve the equation exactly to find i after 0.5 s. exact = A (Round to four decimal places as needed.)
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