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Form a differential equation representi...

Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.`y=a e^(3x)+b e^(-2x)`

Text Solution

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Given,
`=>y=ae^3x+be^(−2)x`
Differentiating,
`=>y′=3ae^3x−2be^(−2)x.......(i)`
`=>y′′=9ae^3x+4be^(−2)x.....(ii)`
Subtracting (ii) from (i)
`=>y′′−y′=9ae^3x+4be^ (−2)-3ae^3x+2be^(−2)x`
...
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