List of top Mathematics Questions on Differential Equations

Let \(y=y(x)\) be solution of the following differential equation \(e^y \frac{dy}{dx} - 2e^y \sin x + \sin x \cos^2 x = 0, y(\pi/2) = 0\). If \(y(0) = \log_e(\alpha + \beta e^{-2})\), then \(4(\alpha + \beta)\) is equal to __________.
The differential equation satisfied by the system of parabolas y² = 4a(x + a) is :
Let f be a twice differentiable function defined on ℝ such that f(0) = 1, f'(0) = 2 and f'(x) ≠ 0 for all x ∈ ℝ. If $| f(x) \ f'(x) | \ | f'(x) \ f''(x) | = 0$, then the value of f(1) lies in the interval :
If \( y = f(x) \) passes through \( (1, 2) \) and \( x \frac{dy}{dx} + y = b x^4 \), then for what value of \( b \), \( \displaystyle \int_{1}^{2} f(x)\,dx = \frac{62}{5} \) ?