Home
Class 12
MATHS
The order of the differential equati...

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 aritrary constants , is :

A

5

B

4

C

3

D

2

Text Solution

AI Generated Solution

The correct Answer is:
To determine the order of the differential equation whose general solution is given by \[ y = (C_1 + C_2) \cos(x + C_3) - C_4 e^{(x + C_5)}, \] we need to identify the number of independent arbitrary constants present in the solution. ### Step-by-Step Solution: 1. **Identify the Constants**: The given solution contains the following arbitrary constants: - \(C_1\) - \(C_2\) - \(C_3\) - \(C_4\) - \(C_5\) 2. **Count the Constants**: We have five constants in total: \(C_1, C_2, C_3, C_4, C_5\). 3. **Determine the Order**: The order of a differential equation is defined as the number of independent arbitrary constants in its general solution. Since we have identified five constants, the order of the differential equation is 5. ### Conclusion: Thus, the order of the differential equation is: \[ \text{Order} = 5 \]
Promotional Banner

Similar Questions

Explore conceptually related problems

The order of the differential equation whose general solution is given by y= (A +B) cos (x +C)+ De^(x) is

The order of the differential equation whose general solution is given by y=(C_(1)+C_(2))sin(x+C_(3))-C_(4)e^(x+(C_(5)) , is

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

The order of the differential equation whose general solution is y = (C_(1) + C_(2)) cos (x + C_(3)) - C_(4)e^(x^(4)) where C_(1), C_(2), C_(3) and C_(4) are arbitrary is

The order of the differential equation whose general solution is y = c_(1) cos 2x + c_(2) cos^(2) x + c_(3) sin^(2) x + c_(4) is

The order of the diferential equation whose general solution is given by y = c_(1)e^(2x+c_(2)) + c_(3)e^(x)+c_(4)sin (x+c_(5)) is

Find the differential equation whose general solution is given by y=(c_(1)+c_(2))cos(x+c_(3))-c_(4)e^(x+c) , where c_(1),c_(2), c_(3), c_(4), c_(5) are arbitary constants.