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If ЁЭТЪ satisfies the equation `(dy)/(dx)=x^2y-1` with `x_0=0, y_0=1` using Taylor’s Series Method find ЁЭТЪ ЁЭТВЁЭТХ ЁЭТЩ= ЁЭЯО.ЁЭЯП (take h=0.1).
рдЙрддреНрддрд░
`(dy)/(dx)=x^2y-1` `x_0=0, y_0=1` ЁЭТЙ=ЁЭЯО.ЁЭЯП
To find : ЁЭТЪ(ЁЭЯО.ЁЭЯП)
`y'=x^2y-1 , y_0'=-1`
`y''=x^2y'+2xy , y_0''=0`
`y'''=x^2y''+2y'x+2y+2xy , y_0'''=0`
Taylor’s series is :
`y=y_0+h.y_0'+h^2/(2!)y_0''+h^3/(3!)y_0'''+...`
∴ ЁЭТЪ(ЁЭЯО.ЁЭЯП)=ЁЭЯП+ЁЭЯО.ЁЭЯП(−ЁЭЯП)+ЁЭЯО+`(0.1)^3/(3!)(2)`
∴ ЁЭТЪ(ЁЭЯО.ЁЭЯП)=ЁЭЯО.ЁЭЯЧЁЭЯОЁЭЯОЁЭЯС
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