MAT136H1 Lecture Notes - Product Rule, Integrating Factor

• School: UTSG
• Department: Mathematics
• Course: MAT136H1
• Professor: all

Document Summary

Question #5 (medium): linear differential equation application to electric circuits. , where is the voltage drop across the capacitor. , then the equation can be written as which is in the form of linear differential equation. Suppose the resistance is , the capacitance is , battery gives constant voltage of , and initial charge is . Find the charge and the current at time . Given kirchhoff"s law, input the numeric values into the parameters in. ; then the integrating factor is sides by 7: Multiply both sides of the equation by the integrating factor: ; the left side is in the form of product rule, thus: ( Plug in these values to evaluate the constant factor: Therefore the charge equation in terms of time is given by: (