The order of the differential equation whose general solution is given by $y = C_{1} e^{2 x + C_{2}} + C_{3} e^{x} + C_{4} s i n (x + C_{5})$ 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 B 4
$y = C_{1} e^{2 x + C_{2}} + C_{3} e^{x} + C_{4} s i n (x + C_{5}) = C_{1} . e^{C_{2}} e^{2 x} + C_{3} e^{x} + C_{4} (s i n x c o s C_{5} + c o s x s i n C_{5}) = A e^{2 x} + C_{3} e^{x} + B s i n x + D c o s x$
Here, $A = C_{1} e^{C_{2}}, B = C_{4} c o s C_{5}, D = C_{4} s i n C_{5}$
(Since equation consists of four arbitrary constants)
$∴$ order of differential equation = 4.

Suggest Corrections

Similar questions

y = C_{1} e^{2 x + C_{2}} + C_{3} e^{x} + C_{4} s i n (x + C_{5})

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

The order of the differential equation whose general solution is given by is

[AMU 2000]

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

Join BYJU'S Learning Program