PYQs Based Test - 10 : Engineering Mathematics

The curve y = f(x) is such that the tangent to the curve at every point (x, y) has a Y-axis intercept c, given by c = -y. Then, f(x) is proportional to

While numerically solving the differential equation $\frac{dy}{dx}+2x{y}^2=0,y\left(0\right)=1$ using Euler’s predictor corrector (improved Euler-Cauchy) with a step size of 0.2, the value of y after the first step is

Consider the differential equation $\frac{dx}{dt}=\sin \left(x\right)$, with the initial condition x(0) = 0. The solution to this ordinary differential equation is

f(z) = (z − 1)⁻¹ − 1 + (z − 1) − (z − 1)² + ⋯ is the series expansion of

Consider the function f(x, y) = x² + y². The minimum value the function attains on the line x + y = 1 (rounded off to one decimal place) is