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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?


By method variation of parameters solve the ODE(D^2+4)y=2 cosec2x?
By method variation of parameter solve the ODE(D^2+4)y=2 cosec2x
Solve the PDE p+q=1

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


Find the general solution of the ordinary differential equation (D2+2D+1)y=e^-xlnx using method of variation of parameters.

p²+q²=4