In which of the following differential equation degree is not defined? (a) `( b ) (c) (d)(( e ) (f) d^(( g )2( h ))( i ) y)/( j )(( k ) d (l) x^(( m )2( n ))( o ))( p ) (q)+3( r ) (s)(( t ) (u) (v)(( w ) dy)/( x )(( y ) dx)( z ) (aa) (bb))^(( c c )2( d d ))( e e )=xlog( f f )(( g g ) (hh) d^(( i i )2( j j ))( k k ) y)/( l l )(( m m ) d (nn) x^(( o o )2( p p ))( q q ))( r r ) (ss) (tt)` (uu) (vv) `( w w ) (xx) (yy)(( z z ) (aaa) d^(( b b b )2( c c c ))( d d d ) y)/( e e e )(( f f f ) d (ggg) x^(( h h h )2( i i i ))( j j j ))( k k k ) (lll)+( m m m ) (nnn)(( o o o ) (ppp) (qqq)(( r r r ) dy)/( s s s )(( t t t ) dx)( u u u ) (vvv) (www))^(( x x x )2( y y y ))( z z z )=xsin( a a a a )(( b b b b ) (cccc) d^(( d d d d )2( e e e e ))( f f f f ) y)/( g g g g )(( h h h h ) d (iiii) x^(( j j j j )2( k k k k ))( l l l l ))( m m m m ) (nnnn) (oooo)` (pppp) (qqqq) `( r r r r ) (ssss) x=sin(( t t t t ) (uuuu) (vvvv)(( w w w w ) dy)/( x x x x )(( y y y y ) dx)( z z z z ) (aaaaa)-2y (bbbbb)),|x|<1( c c c c c )` (ddddd) (eeeee) `( f f f f f ) (ggggg) x-2y=log(( h h h h h ) (iiiii) (jjjjj)(( k k k k k ) dy)/( l l l l l )(( m m m m m ) dx)( n n n n n ) (ooooo) (ppppp))( q q q q q )` (rrrrr)

Options

A. `(d^(2)y)/(dx^(2))+3((dy)/(dx))^(2)=xlog(d^(2)y)/(dx^(2))`
B. `(d^(2)y)/(dx^(2))^(2)+((dy)/(dx))^(2)=xsin(d^(2)y)/(dx^(2))`
C. `x=sin(dy)/(dx)-2y, |x| lt 1`
D. `x-2y=log(dy)/(dx)`

Explanation

To determine in which of the given differential equations the degree is not defined, we need to analyze each option based on the definition of the degree of a differential equation. The degree of a differential equation is defined as the power of the highest derivative when the equation is a polynomial in derivatives.

Let's analyze each option step by step:

### Step 1: Analyze Option (a)
The equation in option (a) is complex and contains derivatives. To determine if the degree is defined, we need to check if it can be expressed as a polynomial in derivatives. If it contains any non-integer powers or transcendental functions of derivatives, the degree is not defined.

**Hint:** Look for non-integer powers or transcendental functions in the derivatives.

### Step 2: Analyze Option (b)
Similar to option (a), we need to check if the equation can be expressed as a polynomial in derivatives. If it contains any non-integer powers or transcendental functions of derivatives, the degree is not defined.

**Hint:** Again, check for non-integer powers or transcendental functions in the derivatives.

### Step 3: Analyze Option (c)
In option (c), we have the equation \( x = \sin\left(\frac{dy}{dx}\right) - 2y \). Here, we can isolate \( \frac{dy}{dx} \) and express it in terms of \( y \) and \( x \). Since this is a first-order equation and can be expressed as a polynomial in \( \frac{dy}{dx} \), the degree is defined.

**Hint:** Isolate the derivative and check if it can be expressed as a polynomial.

### Step 4: Analyze Option (d)
In option (d), we have \( x - 2y = \log\left(\frac{dy}{dx}\right) \). Here, we can also isolate \( \frac{dy}{dx} \) and express it in terms of \( y \) and \( x \). Since this can be expressed in a polynomial form, the degree is defined.

**Hint:** Isolate the derivative and check if it can be expressed as a polynomial.

### Step 5: Analyze Option (e)
In option (e), we have \( x - 2y = \log\left(\frac{dy}{dx}\right) \). Similar to option (d), we can isolate \( \frac{dy}{dx} \) and express it in terms of \( y \) and \( x \). Since this can be expressed in a polynomial form, the degree is defined.

**Hint:** Isolate the derivative and check if it can be expressed as a polynomial.

### Conclusion
After analyzing all the options, we find that the degree is not defined in options (a) and (b) due to the presence of non-integer powers or transcendental functions of derivatives.

Thus, the final answer is:
- The degree is not defined in options (a) and (b).