Separation of Variables: JEE Questions & Solutions

If y=y(x) satisfies the differential equation 16( x+9 x)(4+ 9+ x) y dy=(1+2 y) dx, x0 and y(256)= 2, y(49)=, then 2 is equal to

Let a curve y = f(x) pass through the points (0,5) and ( 2, k). If the curve satisfies the differential equation: 2(3+y)e^2xdx - (7+e^2x)dy…

If y = y(x) is the solution curve of the differential equation (x^2 - 4) dy - (y^2 - 3y) dx = 0, x 2, y(4) = 32, and the slope of the curve…

If the solution curve of the differential equation dydx = x + y - 2x - y passes through the point (2, 1), the value of y(10) equals:

The solution curve y = y(x) of the differential equation (1 + y^2)(1 + (x)) dx + x dy = 0, x 0, passes through the point (1, 1). If y(e) =…

The solution curve of the differential equation: y dxdy = x [( (x)) - ( (y)) + 1 ], with x 0, y 0, passing through the point (e, 1)

The temperature T(t) of a body at time t = 0 is 160^ F. If T(15) = 120^ F, then T(45) is:

If the solution y = y(x) of the differential equation (x^4 + 2x^3 + 3x^2 + 2x + 2) dy = (2x^2 + 2x + 3) dx satisfies y(-1) = - /4, then…

The solution curve of the differential equation 2y dydx + 3 = 5 dydx, passing through the point (0, 1), is a conic whose vertex lies on the…

Let y = y(x) be the solution of the differential equation (x^2 - 3y^2)dx + 3xy dy = 0, y(1) = 1. Then 6y^2(e) is equal to:

Let f be a differentiable function defined on (0, 2) such that f(x) 0 and f(x) + 0^x f(t) 1 - ( e f(t))^2 dt = e, x [0, 2 ]. Then (6 e f (…

Let y = f(x) be the solution of the differential equation y(x + 1) dx - x^2 dy = 0, y(1) = e. Then x 0^+ f(x) is equal to:

The area enclosed by the closed curve C given by the differential equation dydx + x + ay - 2 = 0, y(1) = 0 is 4. Let P and Q be the points…

If the solution curve f(x, y) of the differential equation ((1 + x) dxdy - x x = e^y), x 0, passes through the points (1, 0) and (, 2),…

Let y = y(x) be a solution curve of the differential equation. (1 - x^2 y) dx = y dx + x dy If the line x = 1 intersects the curve y = y(x)…