Differential Equations 1 Question 10

10. The order of the differential equation whose general solution is given by y=(c1+c2)cos(x+c3)c4ex+c5, where c1,c2,c3,c4,c5 are arbitrary constants, is

(a) 5

(b) 4

(c) 3

(d) 2

(1998, 2M)

Objective Questions II

(One or more than one correct option)

Show Answer

Answer:

Correct Answer: 10. (b, c)

Solution:

  1. Given, y=(c1+c2)cos(x+c3)c4ex+c5

y=(c1+c2)cos(x+c3)c4exec5

Now, let c1+c2=A,c3=B,c4ec5=c

y=Acos(x+B)cex

On differentiating w.r.t. x, we get

dydx=Asin(A+B)cex

Again, on differentiating w.r.t. x, we get

d2ydx2=Acos(x+B)cexd2ydx2=y2cexd2ydx2+y=2cex

Again, on differentiating w.r.t. x, we get

d3ydx3+dydx=2cexd3ydx2+dydx=d2ydx2+y

[from Eq. (v)]

which is a differential equation of order 3 .



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