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The solution is:
which is equivalent to
y = K
1
⋅e
–3x
+ K
2
⋅e
5x
+ K
3
⋅e
2x
+ (450⋅x
2
+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 + x
2
⋅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
(
)
.)3/exp()3/exp(5)(
0
33
Cdxxxxy +⋅⋅−⋅=
∫