Question

The order of the differential equation whose general solution is given by $y=(C_1+C_2)cos(x+C_3)-C_4{e}^{x+c_5}$ where $C_1,C_2,C_3,C_4,C_5$ are arbitrary constants, is:

• A. 5
• B. 4
• C. 3
• D. 2

Answer 1

Answer: (C)

3

We can write $y=A+\cos (x+B)-C{e}^x$
where $A=C_1+C_2,B=C_3$ and $C=C_4{e}^{C_5}$
$\frac{dy}{dx}=-A\sin (x+B)-C{e}^x\frac{d^{2}y}{{dx}^2}=-A\cos (x+B)-C{e}^x\Rightarrow \frac{d^{2}y}{{dx}^2}+y=-2C{e}^x\Rightarrow \frac{d^{3}y}{{dx}^3}+\frac{dy}{dx}=-2C{e}^x=\frac{d^{2}y}{{dx}^2}+y\Rightarrow \frac{d^{3}y}{{dx}^3}-\frac{d^{2}y}{{dx}^2}+\frac{dy}{dx}-y=0$
which is differential equation of order 3