Differential Equations Answers

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

Find the integral surface of the equation:

(x²-yz)p+(y²-zx)q =z²-xy

passing through the line x=1 , y=0