![dy/dt = y + sin2t
Solution
rewrite in standard form: y' - y = sin(2t) integrating factor is: e^(-t) e^(-t) y' -
e^(-t) y = e^(-t) sin(2t) [e^(-t) y]' = e^(-t) sin(2t) integrate both sides: e^(-t) y = -1/5 e^(-t)
[sin(2 t) + 2cos(2 t)] + C Solve for y: y = (-1/5)[sin(2 t) + 2cos(2 t)] + Ce^(t)](https://image.slidesharecdn.com/dydtysin2tsolutionrewriteinstandard-230325061914-1aaf5170/85/dydt-y-sin2tSolution-rewrite-in-standard-pdf-1-320.jpg)
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dydt = y + sin2tSolution rewrite in standard.pdf
- 1. dy/dt = y + sin2t Solution rewrite in standard form: y' - y = sin(2t) integrating factor is: e^(-t) e^(-t) y' - e^(-t) y = e^(-t) sin(2t) [e^(-t) y]' = e^(-t) sin(2t) integrate both sides: e^(-t) y = -1/5 e^(-t) [sin(2 t) + 2cos(2 t)] + C Solve for y: y = (-1/5)[sin(2 t) + 2cos(2 t)] + Ce^(t)