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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C 3
$y = (c_{1} + c_{2}) c o s (x + c_{3}) - c_{4} e^{x + c_{5}}$
$= (c_{1} + c_{2}) c o s (x + c_{3}) - c_{4} e^{c^{5}} e^{x}$
Let $c_{1} + c_{2} = c^{1}$
$c_{4} e^{c^{5}} = c^{11}$
$∴ y = c^{1} c o s (x + c_{3}) - c^{11} e^{x}$
Now this equation can be represented in terms g 2 arbitrary constant and order of differential equation $=$ number of arbitrary constant needed to write equation
$= 3$

Suggest Corrections

Similar questions

y = (c_{1} + c_{2}) cos (x + c_{3}) - c_{4} e^{x + c_{5}} .

c_{1} . c_{2}, c_{3}, c_{4}, c_{5}

(c_{1} c o s (x + c_{2})) - (c_{3} e^{- x + c_{4}}) + (c_{5} s i n x)

c_{1}, c_{2}, c_{3}, c_{4}, c_{5}

y = C_{1} e^{x} + C_{2} e^{2 x} + C_{3} e^{3 x} + C_{4} e^{x + c_{5}}

C_{1}, C_{2}, C_{3}, C_{4}, C_{5}

y = (c_{1} c o s (x + c_{2})) - (c_{3} e^{(- x + c_{4})}) + (c_{5} s i n x)

c_{1}, c_{2}, c_{3}, c_{4}, c_{5}

The order of the differential equation whose general
solution is

$y = C_{1} e^{x} + C_{2} e^{2 x} + C_{3} e^{3 x} + C_{4} e^{x + C_{5}}$ where $C_{1}, C_{2}, C_{3}, C_{4}, C_{5}$ are arbitrary
constant is-

Join BYJU'S Learning Program