Differential Equation questions
503 published questions with worked solutions.
- Let f(x) = x - 1 and g(x) = e^x for x R. If dy dx = (e^ -2 x g(f(f(x))) - y x ), y(0) = 0, then y(1) is
- If a curve y = y(x) passes through the point (1, 2 ) and satisfies the differential equation (7x^4 y - e^x cosec y) dx dy = x^5,...
- Let y = y(x) be the solution of the differential equation (x^2 + 1) y' - 2xy = (x^4 + 2x^2 + 1) x, y(0) = 1. Then _ -3 ^ 3 y(x)dx...
- Let the population of rabbits surviving at a time t be governed by the differential equation dp(t) dt = 1 2 p(t) - 200. If p(0) =...
- If a curve y = f(x) passes through the point (1, –1) and satisfies the differential equation, y(1 + xy)dx = x dy, then f (- 1 2 )...
- If (2 + x) dy dx + (y + 1) x = 0 and y(0) = 1, then y ( 2 ) is equal to :
- Let y = y(x) be the solution of the differential equation x dy dx + y x = 4x, x (0, ). If y ( 2 ) = 0, then y ( 6 ) is equal to:
- The differential equation representing the family of ellipse having foci either on the x-axis or on the y-axis, centre at the...
- Let y = y(x) be the solution of the differential equation, (x^2+1)^2 dy dx + 2x(x^2+1)y = 1 such that y(0) = 0. If a ,y(1) = 32 ,...
- Given that the slope of the tangent to a curve y = y(x) at any point (x, y) is 2y x^2 . If the curve passes through the centre of...
- The solution of the differential equation x dy dx + 2y = x^2 (x 0) with y(1) = 1, is:
- Let y = y(x) be the solution of the differential equation, dy dx + y x = 2x + x^2 x, x (- 2 , 2 ), such that y(0) = 1. Then:
- Let y = y(x) be the solution of the differential equation dy dx + 2y = f(x), where f(x) = cases 1, & x [0, 1] 0, & otherwise...
- The curve satisfying the differential equation, (x^2 - y^2) ,dx + 2xy ,dy = 0 and passing through the point (1, 1) is -
- If x dy dx - y x = 6x, (0 < x < 2 ) and y ( 3 ) = 0, then y ( 6 ) is equal to:
- Let f: [0, 1] → R be such that f(xy) = f(x)·f(y), for all x, y ∈ [0, 1], and f(0) ≠ 0. If y = y(x) satisfies the differential...
- If y = y(x) is the solution of the differential equation, x dy dx + 2y = x^2 satisfying y(1) = 1, then y ( 12 ) is equal to:
- Consider the differential equation, y^2dx + (x - 1y )dy = 0. If value of y is 1 when x = 1, then the value of x for which y = 2,...
- If a curve passes through the point (1, −2) and has slope of the tangent at any point (x, y) on it as x^2 - 2y x , then the curve...
- The solution of the differential equation, dy dx = (x - y)^2, when y(1) = 1, is:
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