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If y=a e^(5x)+b e^(-5x), then find diffe...

If `y=a e^(5x)+b e^(-5x),` then find differential equation

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Given `y=*e^(5x)+B*e^(-5x)`
`:. (dy)/(dx)5*Ae^(5x)-5B*e^(-5x)`
`:. (d^(2)y)/(dx^(2))=25Ae^(5x)+25 Be^(-5x)`
`=25(Ae^(5x)+Be^(-5x)`
`(d^(2)y)/(dx^(2))=25y`
`:.` Required differential equation is
`(d^(2)y)/(dx^(2))-25y=0`
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GURUKUL PUBLICATION - MAHARASHTRA PREVIOUS YEAR PAPERS- MARCH 2017-SECTION-II
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