(a) Find the differential equation whose solution is given by
y = eˣ(A cos x + B sin x)
where, A and B are arbitrary constants.
To find the differential equation for (y = e^x(A \cos x + B \sin x)), first calculate the derivatives. Let (y = e^x(A \cos x + B \sin ________ _____ ______ _____ _____ ______ __________ _______ _______.
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(a) Find the differential equation whose solution is given by
y = eˣ(A cos x + B sin x)
where, A and B are arbitrary constants.
(d²y/dx²)¹ᐟ⁵ = k[1+(dy/dx)²]⁵ᐟ²
(a) Which of the following sets are finite, and which are infinite?
(i) The set of points on the circumference of a circle.
(ii) ]0, 1[
(iii) [-1, 1]
(iv) {1, 2, ..., 100}
∫(2eˣ - 3√x)dx
Using the ideal gas equation, estimate the change in the pressure of 1.0 mol of an ideal gas at 0°C when its volume is changed from 22.414 L to 21.414 L.
(a) Evaluate the following limit.
(b) If the law of motion of a particle is given as: s = -t³ + 3t² + 25, then (2+1)
i) find its velocity and acceleration.
ii) find the distance covered by the particle in time t = 5 units
(a) Two coins are tossed simultaneously then find probability of getting at least one head.