# Maple (software) | código de ejemplo en maple

## Código de ejemplo en Maple

• Las siguientes líneas de código calculan la solución exacta de una ecuación diferencial ordinaria de segundo orden:
${\displaystyle {\frac {d^{2}y}{dx^{2}}}(x)-3y(x)=x}$

Sujeto a las condiciones iniciales:

${\displaystyle y(0)=0,\quad \left.{\frac {dy}{dx}}\right|_{y=0}=2}$
dsolve( {diff(y(x),x, x) - 3*y(x) = x, y(0)=0, D(y)(0)=2}, y(x) );

evalf( sqrt(2), 21 );

${\displaystyle {\sqrt {2}}=1{.}41421356237309504880}$
simplify( 35/42 - 5/30 );

${\displaystyle {\frac {35}{42}}-{\frac {5}{30}}={\frac {2}{3}}}$
solve( 3*x^2 + b*x = 7, x );

${\displaystyle -{\frac {b}{6}}+{\frac {\sqrt {b^{2}+84}}{6}},-{\frac {b}{6}}-{\frac {\sqrt {b^{2}+84}}{6}}}$
f := x -> tan(x)*sqrt(x);
D(f)(x);

${\displaystyle (1+\tan(x)^{2}){\sqrt {x}}+{\frac {1}{2}}{\frac {\tan(x)}{\sqrt {x}}}}$
Int( sin(x)^2, x );

${\displaystyle \int {\sin(x)^{2}dx}}$
value( % );

${\displaystyle -{\frac {1}{2}}\sin(x)\cos(x)+{\frac {x}{2}}}$
int( sin(x)^2, x = 0..Pi/2 );

${\displaystyle {\frac {\pi }{4}}}$
• Evaluación de ecuaciones diferenciales lineales en forma simbólica y numérica:
DGL := diff( y(x), x, x ) - 3*y(x) = x:
DGL;

${\displaystyle \left({\frac {d^{2}}{dx^{2}}}y(x)\right)-3y(x)=x}$
dsolve( { DGL, y(0) = 1, D(y)(0) = 2 }, y(x) );

${\displaystyle y(x)=e^$
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