Home
Class 12
MATHS
What is the order of the differential eq...

What is the order of the differential equation whose general solution is `y=c_(1)cos2x+c_(2)sin^(2)x+c_(3)cos^(2)x+c_(4)e^(2x)+c_(5)e^(2x+c6)`?

Text Solution

Verified by Experts

`y=c_(1)cos2x+c_(2)2sin^(2)x+c_(3)cos^(2)x+c_(4)e^(2x)+c_(5)e^(2x+c6)`
`c_(1)cos2x+c_(2)(1-cos2x)/(2)+c_(3)(cos2x+1)/(2) + c_(4)e^(2x)+c_(5)e^(c6)e^(2x)`
`=(c_(1)-c_(2)/2+c_(3)/2)cos2x+(c_(2)/2+c_(3)2)+(c_(4)+c_(5)e^(c6))e^(2x)`
`=lambda_(1)cos2x+lambda_(2)e^(2x)+lambda_(3)`
So, number of artibatry constants in the equation is 3.
Therefore, order of the differential equation will be 3.
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Exercise 10.1|6 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Exercise 10.2|6 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Question Bank|7 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise|337 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Numerical Value Type|3 Videos

Similar Questions

Explore conceptually related problems

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.

Form the differential equation from the following y = e^(x)(A cos 2x + B sin 2x)

Find the differential equation for the following y = e^(3x) (A cos 2x+B sin 2x)

The order of the differential equation whose general solution is given by y=(C_1+C_2)cos(x+C_3)-C_4e^(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

Form the differential equation for y=e^(2x)[A cos 3x-B sin 3x]

General solution of sin^(2) x-5 sin x cos x -6 cos^(2)x=0 is

The differential equation whose general solution is given by y=c_1cos(x+c_2)-c_3e^((-x+c4))+(c_5sinx), where c_1,c_2,c_3,c_4,c_5 are arbitrary constants, is

Which of the following differential equations has y=c_(1)e^(x)+c_(2)e^(-x) as the general solution ?

Which of the following differential equations has y = c_(1)e^(x) + c_(2)e^(-x) as the general solution?

The general solution of the differential equation e^(x) dy + (y e^(x) + 2x)dx = 0 is