Inicio:

>> 2+5

ans =

7

>> 2+5;

>> a=2+5

a =

7

>> b= a^2;

>> b

b =

49

>>

1.-

y=dsolve('Dy = t-y');

>> y

y =

t + C3*exp(-t) - 1

>> y=simplify(y)

y =

t + C3*exp(-t) - 1

>> pretty (y)

t + C3 exp(-t) - 1

>>

>>

>> y=dsolve('Dy = t-y', 'y(1)= 2');

>> y

y =

t + 2*exp(-t)*exp(1) - 1

>> ezplot(y, [0,5])

>> y=dsolve('Dy = t-y');

y

y =

t + C3*exp(-t) - 1

y=simplify(y)

y =

t + C3*exp(-t) - 1

pretty (y)

t + C3 exp(-t) - 1

y=dsolve('Dy = t-y', 'y(1)= 2');

y

y =

t + 2*exp(-t)*exp(1) - 1

ezplot(y, [0,5])

2. Espejo parabólico.

>> ezplot(y,[-5,5]);

>> ezplot(y,[-5,5])

>> y= dsolve('Dy=((y-2)+ sqrt((y-2)^2+t^2))/t','y(0)=1');

>> y

y =

t^2/4 + 1

>> ezplot(y,[-5,5])

3.Cambio de variable independiente.

>> y= dsolve('Dy=((y-2)+ sqrt((y-2)^2+x^2))/x','y(0)=1','x');

>> y

y =

x^2/4 + 1

4* cambio variable independinte.

>> y=dsolve('Dy = x-y', 'y(1)= 2', 'x');

>> y

y =

x + 2*exp(-x)*exp(1) - 1

ejmeplo4

>> y=dsolve('Dy +(y/x) = (exp(x))/x', 'y(1)=2','x');

>> y

y =

exp(x)/x - (exp(1) - 2)/x

>> y=simplify(y)

y =

(exp(x) - exp(1) + 2)/x

>> pretty(y)

exp(x) - E + 2

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x