# Differential equations

1) consider the equation (non-homogenous):

<i> Please see attachment for equation. </i>

? find its general solution

? find the particular solution of this equation, satisfying the initial condition

y(0)=0, y'(0)=0, y''(0)=0

2) find the general solution of the differential equation (non-homogeneous)

<i> Please see attachment for equation. </i>

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#### Solution Preview

see attached file

1) consider the equation (non-honogenous):

----- (1)

â€¢ find its general solution

â€¢ find the particular solution of this equation, satisfying the initial condition

y(0)=0, y'(0)=0, y''(0)=0

aux. Equation is : m^3 - 4m^2 + 3m = 0

m*[m^2 - 4m +3 ] = 0

m*(m-1)*(m-3) = 0

Roots are m1 = 0, m2 = 1, and m3 = 3

Gen. Soln is: yg (x) = C1 + ...

#### Solution Summary

This shows how to find general and particular solutions of differential equations.