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  4. Assertion: Order of the differential equation whose solution is y = c 1 e x + c 2+ c 3 e x + c 4 is 4 . Reason: Order of the differential equation is equal to the number of independent arbitrary constant mentioned in the solution of differential equation.

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Q. Assertion: Order of the differential equation whose solution is $y = c _{1} e ^{ x + c _{2}}+ c _{3} e ^{ x + c _{4}}$ is $4 .$
Reason: Order of the differential equation is equal to the number of independent arbitrary constant mentioned in the solution of differential equation.

Differential Equations

Solution:

$\because y=\left(c_{1} e^{c_{2}}+c_{3} e^{c_{4}}\right) e^{x}=c e^{x}$ (say)
$\therefore \frac{d y}{d x}=c e^{x}=y $
$\therefore $ Order is 1