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The general solution of the differential equation, `y^(prime)+yvarphi^(prime)(x)=0` , where `varphi(x)` is a known function, is (a) `( b ) (c) y=c (d) e^(( e ) (f)-varphi(( g ) x (h))( i ))( j )+varphi(( k ) x (l))-1( m )` (n) (o) `( p ) (q) y=c (r) e^(( s ) (t)+varphi(( u ) x (v))( w ))( x )+varphi(( y ) x (z))-1( a a )` (bb) (cc) `( d d ) (ee) y=c (ff) e^(( g g ) (hh)-varphi(( i i ) x (jj))( k k ))( l l )-varphi(( m m ) x (nn))+1( o o )` (pp) (d) `( q q ) (rr) y=c (ss) e^(( t t ) (uu)-varphi(( v v ) x (ww))( x x ))( y y )+varphi(( z z ) x (aaa))+1( b b b )` (ccc)

A

` y =ce^-phi(x) +phi(x) -1`

B

` y =ce^phi(x) +phi(x)+k`

C

` y =ce^-phi(x) -phi(x) +1`

D

` y =ce^-phi(x) +phi(x) +k`

Text Solution

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The correct Answer is:
A
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MOTION-DIFFERENTIAL EQUATION -Exercise 1
  1. The solution of the differential equation dy =sec^2x dx is -

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  2. The solution of the differential equation dy/dx = (1+x)(1+ y^2) is -

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  3. The general solution of the differential equation, y^(prime)+yvarph...

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  4. The solution of the differential equation (x^(2)+y^(2))dx = 2xy dy is

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  5. The general solution of x(dy)/(dx)=y-xtan((y)/(x)) is . . . .

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  6. x(dy)/(dx)=y(logy-logx+1)

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  7. The solution of the differential equation x^(2) (dy)/(dx)= x^(2) + ...

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  8. The solution of the equation x(dy)/(dx) +3y=x is

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  9. The solution of the differential equation (1+y^(2)) dx = (tan^(-1) ...

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  10. The solution of the differential equation (2x -10 y^3) dy/dx +y =0 is

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  11. The solution of the differential equation dy/dx +y =cosx is -

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  12. The solution of the differential equation (dy)/(dx)+(y)/(x)=x^(2), is

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  13. Number of values of m in N for which y=e^(mx) is a solution of the dif...

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  14. The value of the constant 'm' and 'c' for which y = mx + c is a soluti...

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  15. The general solution of the differential equation dy/dx = (1-x)/y is a...

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  16. Solve sec^(2)x tany dx+sec^(2)y tanx dy=0

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  17. y log ydx-xdy=0

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  18. The solution of the DE x cos y dy = (x e ^(x) log x + e ^(x)) dx is

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  19. Find the orthogonal trajectories of xy=cdot

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  20. Which one of the following curves represents the solution of the initi...

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