HP 49g Function DESOLVE, y(x) = 5 ⋅ exp(− x3 / 3) ⋅ (∫ exp(x3 / 3) ⋅ dx + C0 )

'X^2' ` 'X^3-4*X^2-11*X+30' `LDEC

The solution is:

which can be simplified to

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

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 = (5*INT(EXP(xt^3/3),xt,x)+CC0)*1/EXP(x^3/3))’ }, which simplifies to

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

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