Separation of Variables: JEE Questions & Solutions

If y=y(x) satisfies the differential equation 16√x √(9+√x) (4+√(9+√x))cos y dy=(1+2sin y) dx, x>0 and y(256)=π/2, y(49)=α, then 2sinα is…

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

If y = y(x) is the solution curve of the differential equation (x² - 4) dy - (y² - 3y) dx = 0, x > 2, y(4) = 3/2, and the slope of the…

If the solution curve of the differential equation dy/dx = (x + y - 2)/(x - y), passing through the point (2, 1), is tan⁻¹((y-1)/(x-1)) -…

The solution curve y = y(x) of the differential equation (1 + y²)(1 + log(x)) dx + x dy = 0, x > 0, passes through the point (1, 1). If…

The solution curve of the differential equation: y dx/dy = x [(ln(x)) - (ln(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 (x⁴ + 2x³ + 3x² + 2x + 2) dy = (2x² + 2x + 3) dx satisfies y(-1) = -π/4, then y(0) is…

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

Let y = y(x) be the solution of the differential equation (x² - 3y²)dx + 3xy dy = 0, y(1) = 1. Then 6y²(e) is equal to:

Let f be a differentiable function defined on (0, π/2) such that f(x) > 0 and f(x) + ∫₀^x f(t)√(1 - (logₑ f(t))²) dt = e, ∀ x ∈ [0, π/2].…

Let y = f(x) be the solution of the differential equation y(x + 1) dx - x² dy = 0, y(1) = e. Then lim_(x → 0⁺) f(x) is equal to:

The area enclosed by the closed curve C given by the differential equation dy/dx + (x + a)/(y - 2) = 0, y(1) = 0 is 4π. Let P and Q be the…

If the solution curve f(x, y) = 0 of the differential equation (1 + logₑ x)dx/dy - xlogₑ x = e^y, x > 0 passes through the points (1, 0)…

Let y = y(x) be a solution curve of the differential equation (1 - x² y²) dx = y dx + x dy If the line x = 1 intersects the curve y = y(x)…