The solution of the differential equation dy / dx = sin (x + y) tan (x + y) – 1 is
1) cosec (x + y) + tan (x + y) = x + C 2) x + cosec (x +... View Article
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The solution of differential equation (1 + x)y dx + (1 – y)x dy = 0 is
1) loge (xy) + x – y = C 2) loge (x / y) + x + y = c... View Article
General solution of the differential equation dy / dx = [x + y + 1] / [x + y – 1] is given by
1) x + y = log |x + y| + c 2) x – y = log |x + y|... View Article
The solution of dy / dx = [ax + h] / [by + k] represents a circle, when
1) a = b 2) a = – b ≠ 0 3) a = – 2b = 0 4) a... View Article
Solution of the differential equation xdy – ydx = 0 represents a
1) parabola 2) circle 3) hyperbola 4) straight line Solution: (4) straight line \(\begin{array}{l}\begin{array}{l}x d y-y d x=0 \\ \Rightarrow... View Article
The solution of edy/dx = x, when x = 1 and y = 0 is
1) y = x (log x – 1) + 4 2) y = x (log x – 1)+3 3) y... View Article
A solution of the differential equation (dy / dx)2 – x (dy / dx) + y = 0
1) y = 2x 2) y = – 2x 3) y = 2x – 4 4) y = 2x +... View Article
Which one of the following is the correct solution of (dy / dx) tan y = sin (x + y) + sin (x – y)?
1) sec x = C – 2 sec y 2) sec y = C + 2 cos y 3) sec... View Article
The differential equation of the family of curves y = a cos (x + b) is
1) (d2y / dx2) – y = 0 2) (d2y / dx2) + y = 0 3) (d2y / dx2)... View Article
If y = a sin (5x + c), then
1) dy / dx = 5y 2) dy / dx = – 5y 3) d2y / dx2 = – 25y... View Article
If x = sin t and y = cos pt, then
1) (1 – x2)y2 + xy1 + p2 y = 0 2) (1 – x2)y2 + xy1 – p2 y... View Article
The differential equation of the system of concentric circles with centre (1, 2) is
1) (x – 2) + (y – 1) (dy / dx) = 0 2) (x – 1) + (y –... View Article
The order and degree of the differential equation √sin x (dx + dy) = √cos x (dx – dy) are
1) (1, 2) 2) (2, 2) 3) (1, 1) 4) (2, 1) 5) (0, 1) Solution: (3) (1, 1) √sin... View Article
The differential equation of all straight lines passing through origin is
1) y = √x (dy / dx) 2) dy / dx = y + x 3) dy / dx =... View Article
The differential equation whose solution Ax2 + By2 = 1, where A and B are arbitrary constant is of
1) first-order and second degree 2) first order and first degree 3) second-order and first degree 4) second-order and second... View Article
The differential equation of all parabolas whose axes are parallel to y-axis, is
1) d3y / dx3 = 0 2) d2x / dy2 = c 3) (d3y / dx3) + (d2x / dy2)... View Article
The differential equation of the family of straight lines whose slope is equal to y-intercept, is
1) (x + 1) (dy / dx) – y = 0 2) (x + 1) (dy / dx) + y... View Article
The differential equation representing the family of curves y2 = 2c (x + √c), where c > 0 is a parameter is of order and degree as follows,
1) order 2, degree 2 2) order 1, degree 3 3) order 1, degree 1 4) order 1, degree 2... View Article
The differential equation of the systems of all circles of radius r in the xy-plane is
1) [1 + (dy / dx)3]2 = r2 (d2y / dx2)2 2) [1 + (dy / dx)3]2 = r2 (d2y... View Article
The differential equation of the family of curves y = e2x (a cos x + b sin x), where a and b are arbitrary constants, is given by
1) y2 – 4y1 + 5y = 0 2) 2y2 – y1 + 5y = 0 3) y2 + 4y1... View Article
