KCET Differential Equations — practice questions
26 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice KCET Differential Equations in the app →Order of differential equation:General solution of dy/dx = k y:Variable separable form:For dy/dx = x, general solution:Solve dy/dx = (y/x):Linear DE of first order: dy/dx + P(x) y = Q(x). Solution uses:Integrating factor for dy/dx + y = e^x:Solve dy/dx = -y/x with y(1) = 2:Order and degree of (d²y/dx²)² + y = 0:Homogeneous DE dy/dx = f(y/x): solved by substitutionSolve dy/dx = 1 + y²:For exponential decay (radioactive): dN/dt = -λN. Solution:Solve dy/dx = (x + y)/(x - y) (homogeneous, deg 0):Solve dy/dx + y = sin x:Solve d²y/dx² + y = 0 (SHM):Solve d²y/dx² - 4 dy/dx + 4y = 0:For population growth with carrying capacity (logistic): dP/dt = rP(1 - P/K), the limiting value as t → ∞:For RC circuit charging through resistor R: dq/dt + q/(RC) = V/R. Time constant:Solve x dy/dx + y = x²:Initial value problem: dy/dx = e^x with y(0) = 2. Solution:Order of DE obtained by eliminating constants A, B from y = A e^x + B e^(-x):Solve dy/dx = y² (Bernoulli-like):For Newton's law of cooling, body at 80°C cools in room at 20°C. After time, T = 60°C. Find k if time = 5 min:For DE M(x,y) dx + N(x,y) dy = 0 to be EXACT:Linear independence: two solutions y₁, y₂ of 2nd-order linear DE are independent iff Wronskian W:For DE y'' + 4y = 0, general solution: