Differential Equations Answers

Find the general solutions of the following differential equations using D-operator methods:

(D + 4)² x = sinh 4t

Solve for x in the following set of simultaneous differential equations by using D-operator methods:

(D + 2) x - 3y = 1

-3x + (D + ) y = e^-t

Find the general solutions of the following differential equations using D-operator methods:

(D^2 - 2D + 5) y = x + 5

solve the initial value problem y''-4y'+4y=64sin2t for y(0)=0 and y'(0)=1

Find the complete integral of p - 3 x² = q² - y

find the complete integral and singular integral of 4(1+x³)=9z⁴pq.

two cars each moving at constant speed on a straight road pass a certain point on the road at the same time if car A is moving at 23 m/s and car B is moving at 14 m/s how far apart will they be after five minutes if they contains at the same speed?

1.Solve the differential equation (2𝐷² + 5𝐷 + 2)𝑦 = 𝑒^{-1/ 2 x}

2. Solve the differential equation (𝐷3 − 3𝐷2 + 4𝐷 − 2)𝑦 = 𝑐𝑜𝑠𝗑.

according to newton's law of cooling the rate at which a substance cools in moving air is proportional to the difference between the temperature of the substance and that of the year if the temperature of the year is 298 k a and the substance cools from 478 k to 428 k in 20 minutes. find when the temperature will be 405 k

Solve the following system of equations by using the concept of matrices and determinants. 𝟓𝒙 + 𝟕𝒚 + 𝟐 = 𝟎 𝟒𝒙 + 𝟔𝒚 + 𝟑 = 𝟎 (b) Find whether the following series are convergent or divergent √ 𝟏 𝟒 + √ 𝟐 𝟔 + √ 𝟑 𝟖 + ⋯