Question

The order of the differential equation whose general solution is given by `y=C_(1)e^(2x+C_2)+C_3e^x+C_4sin(x+C_5)` is ______.

Options

• 5

• 4

• 3

• 2

Answer 1

The order of the differential equation whose general solution is given by `y=C_(1)e^(2x+C_2)+C_3e^x+C_4sin(x+C_5)` is 4.

Explanation:

`y=C_(1)e^(2x+C_2)+C_3e^x+C_4sin(x+C_5)`

`=C_1e^(C_2)e^(2x)+C_3e^x+C_4(sinx cos C_5+cosxsinC_5)`

= Ae^2x + C₃e^x + B sinx + D cosx,

where `A=C_1e^(C_2),` B = C₄ cos C₅, D = C₄ sin C₅

This equation consists of four arbitrary constants.

∴ order of differential equation = 4