JEE Main Differential Equations — practice questions
52 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice JEE Main 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:The order of a differential equation is the order of the:The degree of a differential equation (when it is polynomial in derivatives) is the power of the:The order of the differential equation $\dfrac{dy}{dx} + y = 0$ is:The order and degree of $\left(\dfrac{d^2y}{dx^2}\right)^3 + \dfrac{dy}{dx} = 0$ are:A first-order equation of the form $\dfrac{dy}{dx} = f(x)\,g(y)$ is solved by the method of:The general solution of $\dfrac{dy}{dx} = 0$ is:The number of arbitrary constants in the general solution of an $n$-th order differential equation is:The general solution of $\dfrac{dy}{dx} = 2x$ is:The standard form of a first-order linear differential equation is:The degree of the differential equation $\left(\dfrac{dy}{dx}\right)^2 + y = 0$ is:The general solution of $\dfrac{dy}{dx} = e^x$ is:A particular solution of a differential equation is obtained from the general solution by:The order of the differential equation $\dfrac{d^2y}{dx^2} + 3\dfrac{dy}{dx} + 2y = 0$ is:The order of the differential equation $d^3y/dx^3 + (d^2y/dx^2)^2 + y = 0$ is:The general solution of $dy/dx = ky$ is:The integrating factor for $dy/dx + 2y = e^x$ is:A radioactive sample decays following $dN/dt = -\lambda N$. The amount $N(t)$ as a function of time is:The ORDER and DEGREE of the DE (d²y/dx²)³ + (dy/dx)⁵ + y = 0 are:The general solution of a 3rd-order DE contains how many arbitrary constants?The DE dy/dx = y/x is best solved by:For the linear DE dy/dx + (1/x)y = x, the INTEGRATING FACTOR μ(x) is:If a population grows exponentially as dN/dt = 0.1 N (with t in years), the DOUBLING TIME is:By Newton's law of cooling, a hot tea cup at 90°C in a room at 25°C cools so that:For the second-order LDE y'' − 5y' + 6y = 0, the auxiliary equation m² − 5m + 6 = 0 has roots m = 2, 3. The geA mass on a spring obeys d²x/dt² + ω²x = 0 (SHM). The period of oscillation is:Euler's method for a DE y' = f(x, y) computes the next value as: