JEE Advance - Mathematics (1983 - No. 11)
If $$\left( {a + bx} \right){e^{y/x}} = x,$$ then prove that $${x^3}{{{d^2}y} \over {d{x^2}}} = {\left( {x{{dy} \over {dx}} - y} \right)^2}$$
Differentiate the given equation with respect to x and solve for dy/dx.
Differentiate the expression for dy/dx again with respect to x to find d^2y/dx^2.
Substitute the expressions for dy/dx and d^2y/dx^2 into the equation x^3(d^2y/dx^2) = (x(dy/dx) - y)^2 and verify the equality.
Use integration techniques to simplify the given equation.
The equation is incorrect.
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