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The solution of (d v)/(dt)+k/m v=-g is (...

The solution of `(d v)/(dt)+k/m v=-g` is (a) `( b ) (c) v=c (d) e^(( e ) (f) (g) k/( h )g( i ) (j) t (k))( l )-( m )(( n ) mg)/( o ) k (p) (q) (r)` (s) (b) `( t ) (u) v=c-( v )(( w ) mg)/( x ) k (y) (z) (aa) e^(( b b ) (cc) (dd) k/( e e ) m (ff) (gg) t (hh))( i i ) (jj)` (kk) (c) `( d ) (e) v (f) e^(( g ) (h) (i) k/( j ) m (k) (l) t (m))( n )=c-( o )(( p ) mg)/( q ) k (r) (s) (t)` (u) (d) `( v ) (w) v (x) e^(( y ) (z) (aa) k/( b b ) m (cc) (dd) t (ee))( f f )=c-( g g )(( h h ) mg)/( i i ) k (jj) (kk) (ll)` (mm)

A

`v=ce^(-k/mt)-(mg)/k`

B

`v=c-(mg)/ke^(-k/mt)`

C

`ve^(-k/mt)= c-(mg)/k`

D

`ve^(k/mt)=c-(mg)/k`

Text Solution

Verified by Experts

The correct Answer is:
A
`(dv)/(dt) +k/mv=-g`
or `(dv)/(dt) = -k/m(v+(mg)/k)`
or `(dv)/(v+mg//k)=-k/mdt`
or `log(v+(mg)/k)=-k/mt+logc`
or `v+(mg)/k = ce^(-k//mt)`
or `v=ce^(-k/mt)-(mg)/k`
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CENGAGE-DIFFERENTIAL EQUATIONS-Exercise (Single)
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  2. Solve the following differential equations (dy)/(dx)=sinx*siny

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  3. The solution of (d v)/(dt)+k/m v=-g is (a) ( b ) (c) v=c (d) e^(( e...

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  4. The general solution of the differential equation (dy)/(dx)+sin(x+y)/2...

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  5. if y+x(dy)/(dx)=x(phi(xy))/(phi'(xy)) then phi(xy) is

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  6. Find the solution of differential equation x^(2)=1 + (x/y)^(-1) (dy)/(...

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  7. The solution of the differential equation (x+(x^3)/(3!)+(x^5)/(5!)+)/...

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

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  9. A curve passing through (2,3) and satisfying the differential equat...

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  10. The solution of the differential equation (d^2y)/(dx^2)=sin3x+e^x+x^2 ...

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  11. Find the solution of the differential equation y^(')y^(''')=3(y^(''))^...

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  12. The solution of the differential equation y^(prime prime prime)-8y^(pr...

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  13. The slope of the tangent at (x , y) to a curve passing through (1,p...

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

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  15. The solution of differential equation x y^(prime)=x((y^2)/(x^2)+(f((y^...

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  16. The solution of (x^2+x y)dy=(x^2+y^2)dx is (a) ( b ) (c)logx=log(( d ...

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  17. The solution of (y+x+5)dy=(y-x+1)dx is

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  18. The slope of the tangent at (x , y) to a curve passing through a po...

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  19. Solution of the differential equation ydx-xdy+xsqrt(xy)dy=0 is

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  20. The solution of (x^2dy)/(dx)-x y=1+cosy/x is (a) ( b ) (c)tan(( d ) (...

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