HP 50g manual Function Desolve, Variable Odetype

Function DESOLVE

The calculator provides function DESOLVE (Differential Equation SOLVEr) to solve certain types of differential equations. The function requires as input the differential equation and the unknown function, and returns the solution to the equation if available. You can also provide a vector containing the differential equation and the initial conditions, instead of only a differential equation, as input to DESOLVE. The function DESOLVE is available in the CALC/DIFF menu. Examples of DESOLVE applications are shown below using RPN mode.

Example 1 – Solve the first-order ODE:

dy/dx + x2⋅y(x) = 5.

In the calculator use:

'd1y(x)+x^2*y(x)=5' `'y(x)' `DESOLVE

The solution provided is

{‘y(x) = (5*INT(EXP(xt^3/3),xt,x)+cC0)*1/EXP(x^3/3)}’ } , which simplifies to

y(x) = 5 ⋅ exp(−x3 / 3) ⋅ (∫ exp(x 3 / 3) ⋅ dx + C0 ).

The variable ODETYPE

You will notice in the soft-menu key labels a new variable called @ODETY (ODETYPE). This variable is produced with the call to the DESOL function and holds a string showing the type of ODE used as input for DESOLVE. Press @ODETY to obtain the string “1st order linear”.

Example 2 – Solving an equation with initial conditions. Solve

d2y/dt2 + 5y = 2 cos(t/2),

with initial conditions

y(0) = 1.2, y’(0) = -0.5.

In the calculator, use:

[‘d1d1y(t)+5*y(t) = 2*COS(t/2)’ ‘y(0) = 6/5’ ‘d1y(0) = -1/2’] `

‘y(t)’ `

DESOLVE

Notice that the initial conditions were changed to their Exact expressions, ‘y(0) = 6/5’, rather than ‘y(0)=1.2’, and ‘d1y(0) = -1/2’, rather than,

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