If y = (log x)², prove that x²y″ + xy′ = 2.

Question

TextSecond Order Derivative of a FunctionCBSE PYQ

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If x = a sin³ θ, y = b cos³ θ, then find d²y/dx² at θ = π/4.

If y = (tan⁻¹x)², show that (x² + 1)² d²y/dx² + 2x(x² + 1) dy/dx = 2.

If y = (sin⁻¹ x)², then find (1 – x²) d²y/dx² – x dy/dx.

If y = √(ax + b), prove that y(d²y/dx²) + (dy/dx)² = 0.

If f(x) = {ax + b ; 0 < x ≤ 1, 2x² - x ; 1 < x < 2} is a differentiable function in (0, 2), then find the values of a and b.

If x = A cos 4t + B sin 4t, then d²x/dt² is equal to