Differential Equations Answers

Solve

"\\frac{dy}{dx}" =(x+2y-3)/(2x+y-3)

A certain particle falls under gravity in a resisting medium whose resistance varies with velocity.Find the relation between distance and velocity if the initially the particle starts from rest.

Solve the equation. y′′−6y′+9y=0 ;  y(0)=2,y′(0)=−4

a. using differential equation method

b. using Laplace transformation method

By method variation of parameters solve the ODE(D^2+4)y=2 cosec2x?

Solve 𝑥2𝑦``−3𝑥𝑦`+5𝑦=𝑥2sin(𝑙𝑛𝑥) ;𝑦(1)=1,𝑦`(1)=0

Find the power series solution of the differential equation

𝑦``+𝑥𝑦`+(𝑥2+2)𝑦=0

𝑦``+𝑥𝑦`+(𝑥2+2)𝑦=0