HP 50g manual

•the right-hand side of the ODE

•the characteristic equation of the ODE

Both of these inputs must be given in terms of the default independent variable for the calculator’s CAS (typically X). The output from the function is the general solution of the ODE. The examples below are shown in the RPN mode:

Example 1 – To solve the homogeneous ODE

d3y/dx3-4⋅(d2y/dx2)-11⋅(dy/dx)+30⋅y = 0.

Enter:

0` 'X^3-4*X^2-11*X+30'` LDEC µ The solution is (figure put together from EQW screenshots):

where cC0, cC1, and cC2 are constants of integration. This result is equivalent to

y = K1⋅e–3x+ K2⋅e5x + K3⋅e2x.

Example 2 – Using the function LDEC, solve the non-homogeneous ODE:

d3y/dx3-4⋅(d2y/dx2)-11⋅(dy/dx)+30⋅y = x2.

Enter:

'X^2' ` 'X^3-4*X^2-11*X+30'` LDEC µ

The solution is:

which is equivalent to

y = K1⋅e–3x+ K2⋅e5x + K3⋅e2x + (450⋅x2+330⋅x+241)/13500.

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