Eamcet - Maths - Differential Equations

If [x3/(2x-1)(x+2)(x-3)]=A+(B/[2x-1])+(C/[x+2])+(D/[x-3]) then A is equal to

A.  1/2

B.  -(1/50)

C.  -(8/25)

D.  27/25

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If a,b,c ≠ 0 and belong to the set { 0,1,2,3,................9 then log10[(a+10b+102c)/(10-4a+10-3b+10-2c)] is equal to

A.  1

B.  2

C.  3

D.  4

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If x is real, then the minimum value of [(x2-x+1)/(x2+x+1)], is

A.  1/3

B.  3

C.  1/2

D.  1

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x = cos θ, y = sin 5θ  ==>(1-x2) (d2y/dx2)  - x(dy/dx) =

A.  -5y

B.  5y

C.  25y

D.  -25y

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The solution of x log x (dy/dx)+y=2 log x is

A.  y log x=(log  x)2-x+c

B.  y log x=(log  x)2+c

C.  y log x=(log  y)2+c

D.  x log y=(log x)2+c

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The solution of (x2y3+x2)+(y2x3+y2)dy=0 is

A.  (x3+1)(y3+1)=c

B.  (x3-1)(y3-1)=c

C.  (x3-1)(y3+1)=c

D.  (x3+1)(y3-1)=c

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The solution of y2 dx+(3xy-1)dy=0 is

A.  xy3=y2+c

B.  xy3=y2/2+c

C.  xy3=y2/3+c

D.  xy3=x2/2+c

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If y=(x2-1)n, then (x2-1)yn+2+2xyn+1=

A.  (n2+1)yn

B.  (n2-1)yn

C.  n(n2-1)yn

D.  n(n+1)yn

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The solution of excot y dx+(1-ex)cosec2ydy=0 is

A.  (ex+1)cot y=c

B.  (ex-1)cot y=c

C.  (2ex-1)cot y=c

D.   (ex-2)cot y=c

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The solution of (x+y+1) dy/dx=1 is

A.  x+y+2=c ey

B.  x-y+2=c ey

C.  x+y-2=c ey

D.  x+y+2=c e2y

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The solution of x cos(y/x)(y dx+x dy)=y sin y/x(x dy – y dx) is

A.  C xy cos(2y/x)=1

B.  C xy cos(x/y)=1

C.  C xy cos(y/x)=1

D.  C xy cos(y/x)=2

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A family of curves has the differential equation (xy)dy/dx = 2y2 - x2. Then the family of curves is

A.  y2 = cx2 + x3

B.  y2 = x2 + cx4

C.  y2 = cx4 + x3

D.  y2 = x + cx4

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A= sin 780- sin 180+ cos 1320, B= cos 120+ cos 840+ cos 1320+ cos 1560 and C= (sin 750+sin 150)/ (sin 750+cos 150) then by arranging in the ascending order

A.  C,A,B

B.  B,A,C

C.  A,C,B

D.  A,B,C

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The solution of extan y dx+(1-ex)sec2ydy=0 is

A.  Tan y=c(1+ex)

B.  Tan y=c(1-ex)

C.  Tan y=c(1+ex)2

D.  Cos y=c(1-ex)

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If the equation λx2 – 5xy + 6y2 + x -3y=0, represents a pair of straight lines, then their point of intersection is

A.  (-3, -1)

B.  (-1, -3)

C.  (3, -1)

D.  (1, 3)

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If A and B are two square matrices such that B=A-1 BA, then (A+B)2 is equal to

A.  0

B.  A2 + B2

C.  A2 + 2AB+ B2

D.  A + B

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The solution of y dx-x dy+log x dx=0 is

A.  y- log x-1=cx

B.  x+log y+1=cx

C.  y+log x+1=cx

D.  y+log x-1=cx

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The solution of (12x+5y-9)dx+(5x+2y-4)dy=0 is

A.  6x2+5xy+y2+9x+4y=c

B.  6x2+5xy+y2-9x-4y=c

C.  6x2-5xy-y2-9x-4y=c

D.  3x2+5xy+2y2-9x-4y=c

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The solution of (x+y+1)dx+(3x+4y+4)dy=0 is

A.  x-2y-2=c ex/(2x+4y+4)

B.  x+2y-3=c ex/(2x+4y+4)

C.  x-2y-2=c ex/(2x+4y+4)

D.  x-2y+2=c ex/(2x+4y+4)

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Solution of differential equation dy/dx = (1+y2) (1+x2)-1is

A.  y-x=c(1+xy)

B.  y+x=c(1+xy)

C.  y+x=c(1-xy)

D.  y-x=c(1-xy)

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The line 4x + 6y + 9=0, touches the parabola y2=4x at the point

A.  (-3, 9/4)

B.  (3, -9/4)

C.  (9/4, -3)

D.  (-9/4, -3)

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The solution of 3excos2ydx+(1-ex)cot y dy=0 is

A.  Tan y=c(ex-1)3

B.  Tan y=c(ex+1)3

C.  Tan y=c(ex-1)2

D.  Cos y=c(ex-1)3

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x2+y2=t+(1/t),x4+y4=t2+(1/t2)⇒x3y(dy/dx)=

A.  -1

B.  1

C.  0

D.  t

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The radius of the circle r2-2√2r(cos θ + sin θ)-5=0 is

A.  0

B.  3

C.  2

D.  5

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The solution of (1+ex/y)dx+ex/y(1-x/y)dy=0 is

A.  yey/x+x=c

B.  yey/x-x=c

C.  yey/x+y=c

D.  yey/x+x=c

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The solution ofn(ex+1)y dy+(y+1)dx=0 is

A.  ex+y=c(y+1)(ex+1)

B.  ex+y=c(y+1)(ex-1)

C.  ex+y=c(y-1)(ex+1)

D.  ex+y=c(y-1)(ex-1)

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The curve represented by X= 2( cos t + sin t ), y=( cos t - sin t ) is

A.  a circle

B.  a parabola

C.  an ellipse

D.  hyperbola

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The solution of ex-y dx+ey-x dy=0 is

A.   e2x-e2y=c

B.  e2x+e2y=c

C.  ex+ey=c

D.  ex-ey=c

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