अवकल समीकरण `(dy)/(dx)=e^(ax)cosy` को हल कीजिये यदि y(0)=0

Explanation

`(dy)/(dx)=e^(ax)cosy`
`implies(dy)/(cosy)=e^(ax)dx`
`impliessecydy=e^(ax)dx`
समाकलन से,
`intsecydy=inte^(ax)dx+c`
`implieslog(secy+tany)=(1)/(a)e^(ax)+c`
`impliesalog(secy+tany)=e^(ax)+k" ".......(1)`
प्रश्नानुसार, यदि x=0 तब y=0
`impliesalog(sec0+tan0)=e^0+k`
`impliesalog(1+0)=1+k`
`impliesk=-1`
अतः समीकरण (1) से,
`alog(secy+tany)=e^(ax)-1`