AP EAPCET (Engineering) Differential Equations — practice questions
81 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice AP EAPCET (Engineering) Differential Equations in the app →The **order** of a differential equation is:The order and degree of $x^2 \dfrac{d^2y}{dx^2} + 3x \dfrac{dy}{dx} + 4y = 0$ are respectively:The **general solution** of a differential equation contains:The integrating factor for the linear DE $\dfrac{dy}{dx} + P(x)y = Q(x)$ is:To solve a **homogeneous** differential equation of degree 1 (e.g. $dy/dx = f(y/x)$), the standard substitutioThe order of the differential equation obtained by eliminating the arbitrary constants $A$ and $B$ from $y = AThe order and degree of $ qrt{1 + (dy/dx)^2} = d^2y/dx^2$ are:Eliminate the arbitrary constant from $y^2 = 4ax$ to form the DE:The DE obtained by eliminating $c_1$ and $c_2$ from $y = c_1 e^{3x} + c_2 e^{2x}$ is:Solve $\dfrac{dy}{dx} = \dfrac{1 + y^2}{1 + x^2}$.Solve $\dfrac{dy}{dx} = e^{x+y}$.The DE $y - x \dfrac{dy}{dx} = 0$ has general solution:The general solution of $\dfrac{dy}{dx} + y = e^{-x}$ is:Solve the homogeneous DE $x\,dy/dx = x\,\tan(y/x) + y$:The differential equation of the family of straight lines $y = mx + c$ (with $m, c$ arbitrary) is:Solve $ ec^2 x \cdot \tan y \, dx + ec^2 y \cdot \tan x \, dy = 0$:Solve $\dfrac{dy}{dx} = \dfrac{y + qrt{x^2 + y^2}}{x}$.The half-life of a radioactive substance decaying by $dm/dt = -km$ (with $k > 0$) in terms of $k$ is:Newton's law of cooling: $dT/dt = -k(T - T_s)$ where $T_s$ is the surrounding temperature. The general solutioSolve $(x^2 - y^2)\,dx + 2xy\,dy = 0$.The particular solution of $\dfrac{dy}{dx} + y\tan x = ec x$ given $y(0) = 1$ is:If $y = e^x \cos x$, then $\dfrac{d^2 y}{dx^2} - 2\dfrac{dy}{dx} + 2y$ equals: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:Which kind of equation has a function, not a number, as its solution?Derivatives in several variables occur in which equation type?For y'' + sin(y') = 0, which statement about order and degree is correct?Which differential equation has y = e^(-3x) as a solution?Which function satisfies x (dy/dx) = 2y?What is a solution of a differential equation that contains arbitrary constants called?A solution obtained by giving particular values to the arbitrary constants is called what?How many arbitrary constants are in the general solution of a fourth order equation?The curve y = f(x) that satisfies a differential equation is called what?The variable separable method applies when terms in y can be gathered with which differential?The general solution of dy/dx = y/x (x, y positive) is which of these?Find the curve through (0, 2) whose slope at every point (x, y) is 3x^2.Find the curve through (1, 1) given x dy = (2x^2 + 1) dx, with x > 0.Find the curve through (0, 2) satisfying dy/dx = x/y.Find y when dy/dx = y and y = 3 at x = 0.At 5 percent continuous interest, Rs 1000 deposited grows to what after 10 years?With interest at r percent compounded continuously, the doubling time in years is what?A quantity whose rate of growth is proportional to its size follows which law?A function F(x, y) is homogeneous of degree n if F(lambda x, lambda y) equals what?What is the degree of homogeneity of (x^3 + y^3)/(xy)?Which equation is a homogeneous differential equation?Which substitution is used to solve dy/dx = F(y/x)?For a homogeneous equation written as dx/dy = F(x/y), which substitution is convenient?Solve dy/dx = y/x + tan(y/x) for the general solution.In dy/dx + Py = Q, a first order linear form, P and Q are what?For dy/dx + Py = Q, the integrating factor is which expression?For a linear equation dx/dy + P1 x = Q1, what must P1 and Q1 be?Find the integrating factor of y dx + (x - y^3) dy = 0, treating x as dependent.The date of birth of differential equations is taken as 11 November of which year?What do derivatives in a differential equation usually stand for?What does a partial differential equation contain?A differential equation is (d²y/dx²)³ + (dy/dx)⁴ + y = 0. What are its order and degree?For (d³y/dx³)² + (dy/dx)⁵ = x, find the order and degree.