Question and Answers Forum

All Questions      Topic List

Differential Equation Questions

Previous in All Question      Next in All Question      

Previous in Differential Equation      Next in Differential Equation      

Question Number 208264 by efronzo1 last updated on 09/Jun/24

$$\cancel{\underset{―}{\underbrace{}}}$$

Answered by mr W last updated on 10/Jun/24

$$let{y}^{\prime }=p$$$$p^{\prime }-2p=2(e^x\cos x-1)$$$$p=\frac{2\int e^{-2x}(e^x\cos x-1)dx+C_1}{e^{-2x}}$$$$=\frac{e^{-x}(\sin x-\cos x)+e^{-2x}+C_1}{e^{-2x}}$$$$=e^x(\sin x-\cos x)+1+C_1{e}^{2x}$$$$y=\int [e^x(\sin x-\cos x)+1+C_1{e}^{2x}]dx$$$$\Rightarrow y=-e^x\cos x+x+C_1{e}^{2x}+C_2$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com