## anonymous one year ago eliminate the arbitrary constant y=c1x=c2e^2x

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1. anonymous

can you help me?

2. anonymous

3. Loser66

I guess!! it is $$y = C_1x+C_2e^{2x}$$ and it is a solution of a DE. If it is so, to eliminate the constants, you need initial values, like y(0) = a, and y'(0) =b.

4. anonymous

$y=c1x+c2 e ^{2x} ...(1)$ diff. twice w.r.t x $y \prime=C1+2 C2 e ^{2x} ...(2)$ $y \prime \prime=0+4C2 e ^{2x} ...(3)$ from (3) $C2=\frac{ y \prime \prime }{ 4~e ^{2x} }$ put in (2) $y \prime=C1+2 e ^{2x}*\frac{ y \prime \prime }{ 4~e ^{2x} }$ $C1=y \prime-\frac{ y \prime \prime }{ 2 }$ put the values of C1 and C2 in (1)