Differential Equations Answers

A thermometer is taken from a room where the temperature is 20°C to the outdoors,

where the temperature is 5°C. After one minute the thermometer read 12°C.Use

Newton’s Law of Cooling to answer the following questions:

a) What will the reading on the thermometer be after one more minute?

b) When will the thermometer read 6°C?

Find a power series solution of xy'=y

A string of iength L is stretched and fastened to two fix points. Find the solution of

the r.{ave equatiorl (vibrating string) ytt = a^2.yxx, when initial displacernent

y(x,0) = f (x) = b sin (pi.x / t).

also find the Fourier cosine transformation of exp(-x^2)

(D ^ 2 + 3D + 2) * y = sin 2x + 5 degrees + log 3

A tank with a horizontal sectional area constant at 10 square meter and 4 m high contains water to a depth of 3.5 m. the tank has a circular orifice 5 cm in diameter and located at its side 0.5 m above the bottom. if the coefficient of discharge of the orifice is 0.60, find the duration of flow though the orifice.

Find the solution of the following symmetrical simultaneous differential equation dx/1 = -dy/1 = dz/1

For the following differential equation locate and classify its singular points on the x-axis x^2 y" + (2-x)y' = 0.

Find a power series solution of xy'=y​

Show that 𝑦=𝑐1𝑒𝑥+𝑐2𝑒2𝑥 is the general solution of 𝑦′′−3𝑦′+2𝑦=0 on any interval, and find the particular solution for which 𝑦 0 =−1 and 𝑦′(0)=1. 

Using Charpit’s method, solve:

P²+ q² -2px -2qy +1=0