Separation yields −1/y=x+C; y(1)=−1 gives C=0, hence the expression y=−1/x. Substituting −2 gives the officially intended value 0.5. There is a domain caveat: the initial-value solution through x=1 has maximal interval x>0 and cannot pass through the pole at x=0. Thus 0.5 is the value of the continued algebraic expression on the other interval, not a value on the same connected IVP solution.
More Differential Equations: First order linear ODEs and higher order linear ODEs with constant coefficients questions
GATE 2024 AE Q12– The acceleration of a body travelling in a straight line is given by a = -C 1 - C 2v2…
GATE 2024 AE Q36– Given y = epx qx, where p and q are non-zero real numbers, the value of the differential…
GATE 2025 AE Q43– Consider the ordinary differential equation: 12dydx + yx = 1. If y = 2/3 at x = 1, then…
GATE 2026 AE Q49– Consider the differential equation with the initial conditions given below. If y(x) is the…
GATE 2026 AE Q50– An object of mass 1 kg is launched with an initial speed of v o into a large tank filled…
GATE 2023 AE Q42– For dy/dx+ay= x, with constants a,ω and y(0)=1, select true statements as x.