Differential Equation questions
503 published questions with worked solutions.
- If y(x) is the solution of the differential equation dy dx + ( 2x + 1 x )y = e^ -2x , x > 0, where y(1) = 12e^ -2 , then:
- The curve amongst the family of curves represented by the differential equation, (x^2 - y^2)dx + 2xy ,dy = 0 which passes through...
- The general solution of the differential equation (y^2 - x^3)dx - xy ,dy = 0 (x ≠ 0) is: (where c is a constant of integration)
- If dy dx = xy x^2+y^2 ; y(1) = 1; then a value of x satisfying y(x) = e is -
- If for x 0, y = y(x) is the solution of the differential equation, (x+1)dy=((x+1)^2+y-3) ,dx, y(2) = 0, then y(3) is equal to...
- If x^3dy+xy ,dx=x^2dy+2y ,dx ; y(2) = e and x > 1, then y(4) is equal to -
- If dx dy = 1 + x - y^2 y , x(1) = 1, then 5x(2) is equal to ______.
- Let y = y(x) be the solution of the differential equation dy dx = 2x(x + y)^3 - x(x + y) - 1, y(0) = 1. Then ( 1 2 + y ( 1 2 )...
- If x = x(t) is the solution of the differential equation (t + 1)dx = (2x + (t + 1)^4)dt, x(0) = 2, then, x(1) equals _____.
- Let y = y(x) be the solution of the differential equation (x² + 4)² dy + (2x³y + 8xy − 2)dx = 0. If y(0) = 0, then y(2) is equal...
- Let y = y(x) be the solution of the differential equation (x + y + 2)² dx = dy, y(0) = −2. Let the maximum and minimum values of...
- If the solution y = y(x) of the differential equation (x^4 + 2x^3 + 3x^2 + 2x + 2)dy - (2x^2 + 2x + 3)dx = 0 satisfies y(-1) = -...
- Let the solution y = y(x) of the differential equation dy dx - y = 1 + 4 x satisfy y(π) = 1. Then y ( 2 ) + 10 is equal to ______...
- If y = y(x) is the solution of the differential equation dy dx + 2y = (2x), y(0) = 34, then y ( 8 ) is equal to:
- The differential equation of the family of circles passing the origin and having center at the line y = x is:
- Let y = y(x) be the solution of the differential equation dy dx + 2x (1 + x^2)^2 y = xe^ 1 (1 + x^2) ; y(0) = 0. Then the area...
- Let y = y(x) be the solution of the differential equation (1 + x^2) dy dx + y = e^ ^ -1 x , y(1) = 0. Then y(0) is
- Let y = y(x) be the solution of the differential equation (2x _ex) dy dx + 2y = 3x _ex, x > 0 and y(e⁻¹) = 0. Then, y(e) is equal...
- If y = y(x) is the solution of the differential equation, e^y ( dy dx -1 )=e^x such that y(0) = 0, then y(1) is equal to :
- Let y = y(x) be a solution of the differential equation, 1-x^2 dy dx + 1-y^2 =0, |x| < 1. If y ( 1 2 )= 3 2 , then y ( -1 2 ) is...
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