General solution of dy/dx = k y:
Ay = kx + C
By = C × e^(kx) (exponential)
Cy = x²
Dy = k
Answer & Solution
Correct answer: B. y = C × e^(kx) (exponential)
dy/y = k dx → ln|y| = kx + C → y = A e^(kx). Famous equation of exponential growth (k > 0) or decay (k < 0). Models population, radioactivity, capacitor discharge.
Related questions
Reducing $(2x-1)\dfrac{d^2y}{dx^2}-2\dfrac{dy}{dx}=0$ with $y=2$ and $\dfrac{dy}{dx}=3$ atA village grows at a rate proportional to its population. It was 20,000 in 1999 and 25,000For $\dfrac{d^2y}{dx^2}+3\dfrac{dy}{dx}+2y=6e^{x}+ in x$, the particular integral is:The complementary function of $\dfrac{d^2y}{dx^2}+3\dfrac{dy}{dx}+2y=6e^{x}+ in x$ is:Solutions of a differential equation form a set that is a:The power counted for the degree must be a whole number that is:An equation whose highest derivative is the third has order:The study at this stage is confined to equations that are: