Consider the following statement 1. The general solution of ` (dy)/(dx) =f (x) +x` is of the form y = f(x) +c , where c is an arbitary constant. 2. The degree of `((dy)/(dx))^(2) = f(x) " is " 2` which of the above statements is/are correct ?

Options

A. 1 only
B. 2 only
C. Both 1 and 2
D. Neither 1 nor 2

Answer

D

Explanation

statement 1:
The general solution of ` (dy)/(dx) = f(x) +x`
Now integrating on both side
` int (dy)/(dx) = int [f (x) +x] dx`
y = f(x) +C
Statement 1 is correct
Statement 2 :
` (dy)/(dx) = f(x)+c`
Squaring both sides,
` ((dy)/(dx))^(2) = (f (x) +c )^(2)`
` ((dy)/(dx))^(2) = [ f(x)^(2) + 2cf (x) +c^(2) ]`
Hence, the differential equation is of order -1 and degree -2.
both statement 1 and 2 are correct.
Statement 2.
` (dy)/(dx) = f(x) +c`
Squaring both sides,
`((dy)/(dx))^(2) = (f(x) +c)^(2)`
` ((dy)/(dx))^(2) = [ f(x)^(2) + 2cf(x) +c^(2)]`
Hence the differential equation is of order -1and degree -2.
both statement 1 and 2 are correct option (C) is correct.