Homogeneous Differential Equations: JEE Questions & Solutions

Let the solution curve of the differential equation x dy - y dx = √(x²+y²) dx, x>0, with y(1)=0, be y=y(x). Then y(3) is equal to

Let x = x(y) be the solution of the differential equation: y = ( x - y dx/dy) sin( x/y), y > 0 and x(1) = π/2. Then cos(x(2)) is equal to:

If sin(y/x) = ln|x| + α/2 is the solution of the differential equation x cos(y/x) dy/dx = y cos(y/x) + x, and y(1) = π/3, then α² is equal…

The solution of the differential equation dy/dx = -((x² + 3y²)/(3x² + y²)), y(1) = 0 is:

Let y = y(x) be the solution of the differential equation (3y² - 5x²) y dx + 2x(x² - y²) dy = 0, such that y(1) = 1. Then ( y(2))³ - 12y(2)…

The slope of the tangent at any point (x, y) on a curve y = y(x) is (x² + y²)/2xy, x > 0. If y(2) = 0, then a value of y(8) is: