Question #297219

Y=c1e^x+c2e^2x y"-2y+3y=0

1
Expert's answer
2022-02-14T16:45:43-0500

Solution:

To check whether y=c1ex+c2e2xy=c_1e^x+c_2e^{2x} is the solution of y2y+3y=0y''-2y+3y=0...(i)

Now, y=c1ex+c2e2xy=c_1e^x+c_2e^{2x}

y=c1ex+2c2e2xy=c1ex+4c2e2xy'=c_1e^x+2c_2e^{2x} \\ y''=c_1e^x+4c_2e^{2x}

Put these in LHS of (i),

=y2y+3y=c1ex+4c2e2x2(c1ex+2c2e2x)+3(c1ex+c2e2x)=2c1ex+3c2e2x0=y''-2y+3y \\=c_1e^x+4c_2e^{2x}-2(c_1e^x+2c_2e^{2x})+3(c_1e^x+c_2e^{2x}) \\=2c_1e^x+3c_2e^{2x} \\\ne0

So, it is not the solution of given D.E.


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