The solution of the differential equation `y^-8y^=0,` where `y(0)=1/8,y^(prime)(0)=0,y^(0)=1` , is (a) `( b ) (c) y=( d )1/( e )8( f ) (g)(( h ) (i) (j)(( k ) (l) e^(( m ) (n)8x (o))( p ))/( q )8( r ) (s)+x-( t )7/( u )9( v ) (w) (x))( y )` (z) (aa) `( b b ) (cc) y=( d d )1/( e e )8( f f ) (gg)(( h h ) (ii) (jj)(( k k ) (ll) e^(( m m ) (nn)8x (oo))( p p ))/( q q )8( r r ) (ss)+x+( t t )7/( u u )8( v v ) (ww) (xx))( y y )` (zz) (aaa) `( b b b ) (ccc) y=( d d d )1/( e e e )8( f f f ) (ggg)(( h h h ) (iii) (jjj)(( k k k ) (lll) e^(( m m m ) (nnn)8x (ooo))( p p p ))/( q q q )8( r r r ) (sss)-x+( t t t )7/( u u u )8( v v v ) (www) (xxx))( y y y )` (zzz) (d) None of these

The solution of the differential equation y''-8y''=0, where y(0)=(1)/(8),y'(0)=0,y^(0)=1, is

The solution of the differential equation y^(primeprimeprime)-8y^(primeprime)=0, where y(0)=1/8,y^(prime)(0)=0,y''(0)=1 , is

The solution of the differential equation y^(primeprimeprime)-8y^(primeprime)=0, where y(0)=1/8,y^(prime)(0)=0,y''(0)=1 , is

The solution of the differential equation {1+xsqrt((x^2+y^2))}dx+{sqrt((x^2+y^2))-1}ydy=0 is equal to (a) ( b ) (c) (d) x^(( e )2( f ))( g )+( h )(( i ) (j) y^(( k )2( l ))( m ))/( n )2( o ) (p)+( q )1/( r )3( s ) (t) (u) (v)(( w ) (x) (y) x^(( z )2( a a ))( b b )+( c c ) y^(( d d )2( e e ))( f f ) (gg))^(( h h ) (ii) (jj)3/( k k )2( l l ) (mm) (nn))( o o )=c (pp) (qq) (rr) ( s s ) (tt) x+( u u )(( v v ) (ww) y^(( x x )3( y y ))( z z ))/( a a a )3( b b b ) (ccc)+( d d d )1/( e e e )2( f f f ) (ggg) (hhh) (iii)(( j j j ) (kkk) (lll) x^(( m m m )2( n n n ))( o o o )+( p p p ) y^(( q q q )2( r r r ))( s s s ) (ttt))^(( u u u ) (vvv) (www)1/( x x x )2( y y y ) (zzz) (aaaa))( b b b b )=c (cccc) (dddd) (eeee) ( f f f f ) (gggg) x-( h h h h )(( i i i i ) (jjjj) y^(( k k k k )2( l l l l ))( m m m m ))/( n n n n )2( o o o o ) (pppp)+( q q q q )1/( r r r r )3( s s s s ) (tttt) (uuuu) (vvvv)(( w w w w ) (xxxx) (yyyy) x^(( z z z z )2( a a a a a ))( b b b b b )+( c c c c c ) y^(( d d d d d )2( e e e e e ))( f f f f f ) (ggggg))^(( h h h h h ) (iiiii) (jjjjj)3/( k k k k k )2( l l l l l ) (mmmmm) (nnnnn))( o o o o o )=c (ppppp) (qqqqq)

The solution of the differential equation {1+xsqrt((x^2+y^2))}dx+{sqrt((x^2+y^2))-1}ydy=0 is equal to (a) ( b ) (c) (d) x^(( e )2( f ))( g )+( h )(( i ) (j) y^(( k )2( l ))( m ))/( n )2( o ) (p)+( q )1/( r )3( s ) (t) (u) (v)(( w ) (x) (y) x^(( z )2( a a ))( b b )+( c c ) y^(( d d )2( e e ))( f f ) (gg))^(( h h ) (ii) (jj)3/( k k )2( l l ) (mm) (nn))( o o )=c (pp) (qq) (rr) ( s s ) (tt) x+( u u )(( v v ) (ww) y^(( x x )3( y y ))( z z ))/( a a a )3( b b b ) (ccc)+( d d d )1/( e e e )2( f f f ) (ggg) (hhh) (iii)(( j j j ) (kkk) (lll) x^(( m m m )2( n n n ))( o o o )+( p p p ) y^(( q q q )2( r r r ))( s s s ) (ttt))^(( u u u ) (vvv) (www)1/( x x x )2( y y y ) (zzz) (aaaa))( b b b b )=c (cccc) (dddd) (eeee) ( f f f f ) (gggg) x-( h h h h )(( i i i i ) (jjjj) y^(( k k k k )2( l l l l ))( m m m m ))/( n n n n )2( o o o o ) (pppp)+( q q q q )1/( r r r r )3( s s s s ) (tttt) (uuuu) (vvvv)(( w w w w ) (xxxx) (yyyy) x^(( z z z z )2( a a a a a ))( b b b b b )+( c c c c c ) y^(( d d d d d )2( e e e e e ))( f f f f f ) (ggggg))^(( h h h h h ) (iiiii) (jjjjj)3/( k k k k k )2( l l l l l ) (mmmmm) (nnnnn))( o o o o o )=c (ppppp) (qqqqq)

The solution of the differential equation (dy)/(dx)=(3x^2y^4+2x y)/(x^2-2x^3y^3) is (a) ( b ) (c) (d)(( e ) (f) y^(( g )2( h ))( i ))/( j ) x (k) (l)-( m ) x^(( n )3( o ))( p ) (q) y^(( r )2( s ))( t )=c (u) (v) (w) ( x ) (y) (z)(( a a ) (bb) x^(( c c )2( d d ))( e e ))/( f f )(( g g ) (hh) y^(( i i )2( j j ))( k k ))( l l ) (mm)+( n n ) x^(( o o )3( p p ))( q q ) (rr) y^(( s s )3( t t ))( u u )=c (vv) (ww) (xx) ( y y ) (zz) (aaa)(( b b b ) (ccc) x^(( d d d )2( e e e ))( f f f ))/( g g g ) y (hhh) (iii)+( j j j ) x^(( k k k )3( l l l ))( m m m ) (nnn) y^(( o o o )2( p p p ))( q q q )=c (rrr) (sss) (d) ( t t t ) (uuu) (vvv)(( w w w ) (xxx) x^(( y y y )2( z z z ))( a a a a ))/( b b b b )(( c c c c )3y)( d d d d ) (eeee)-2( f f f f ) x^(( g g g g )3( h h h h ))( i i i i ) (jjjj) y^(( k k k k )2( l l l l ))( m m m m )=c (nnnn) (oooo)

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)

The solution of the differential equation (d^2y)/(dx^2)=sin3x+e^x+x^2 when y_1(0)=1 and y(0) is (a) ( b ) (c) (d)(( e )-sin3x)/( f )9( g ) (h)+( i ) e^(( j ) x (k))( l )+( m )(( n ) (o) x^(( p )4( q ))( r ))/( s )(( t ) 12)( u ) (v)+( w )1/( x )3( y ) (z) x-1( a a ) (bb) (cc) ( d d ) (ee) (ff)(( g g )-sin3x)/( h h )9( i i ) (jj)+( k k ) e^(( l l ) x (mm))( n n )+( o o )(( p p ) (qq) x^(( r r )4( s s ))( t t ))/( u u )(( v v ) 12)( w w ) (xx)+( y y )1/( z z )3( a a a ) (bbb) x (ccc) (ddd) (eee) ( f f f ) (ggg) (hhh)(( i i i )-cos3x)/( j j j )3( k k k ) (lll)+( m m m ) e^(( n n n ) x (ooo))( p p p )+( q q q )(( r r r ) (sss) x^(( t t t )4( u u u ))( v v v ))/( w w w )(( x x x ) 12)( y y y ) (zzz)+( a a a a )1/( b b b b )3( c c c c ) (dddd) x+1( e e e e ) (ffff) (d) None of these