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  4. The order of the differential equation y = C1eC2 + x + C3 eC4 + x is

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Q. The order of the differential equation $y = C_1e^{C_2 + x} + C_3 e^{C_4 + x}$ is

KCETKCET 2019Differential Equations

Solution:

$y=c_{1}e^{c_{2}+x}+c_{3}e^{c_{4}+x}$
$=\left(c_{1}e^{c_{2}}+c_{3}e^{c_{4}}\right)e^{x}$
$=Ae^{x}$
$\frac{dy}{dx}-Ae^{x}=y$
$\Rightarrow \, order \,= 1$