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Question

From the differential equation to the family of curves y=ae2x+be3x by eliminating arbitrary constants a and b.

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Solution

y=ae27+be3x(i)
y1=2ae2x+3be3x(ii)
y2=4ae27+9be3x(iii)

Eqn(ii)+2xEqn(i)weget Eqn(iii)3Eqn(ii)weget
y1+2y=5be3x y23y=10ae2x
[be3x=15(y1+2yy)] [ae2x=110(y23y1)]
putting vasues of ae2x & be3xineqn(i)
y=15(y1+2y)+110(y23y1)
10y=2y1+4y+y23y1
10y=5y2y1
[10y+y15y2=0]

1175123_1347420_ans_1d5c2db748df4c29af493c2e2e9a1ff5.jpg

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