>	with(DEtools);

Opg 1

>	ode1:=diff(y(x),x,x) + diff(y(x),x) - 6*y(x) = exp(2*x);

>	ans1:=dsolve(ode1);

Opg 2

>	ode2:=diff(y(x),x,x) + 2*diff(y(x),x) + 2*y(x) = 2;

>	ans2:=dsolve(ode2);

Opg 3

>	ode3:=diff(y(x),x,x) + y(x) = cos(x);

>	ans3:=dsolve(ode3);

Opg 4

>	ode4:=diff(y(x),x,x)+9*y(x)=80*cos(5*x);

>	ans4:=dsolve({ode4,y(0)=0,D(y)(0)=0});

Opg 5

>	ode5:=diff(y(x),x,x)-4*diff(y(x),x)+4*y(x)=0;

>	ans5a:=dsolve(ode5);

>	ans5b:=dsolve({ode5,y(0)=0,D(y)(0)=2});

Opg 6

>	ode6:=diff(y(x),x,x)-2*diff(y(x),x)+y(x)=x;

>	dsolve(ode6);

Opg 7

>	ode7:=diff(y(x),x)=3*x^2*exp(-y(x));

>	odeadvisor(ode7);

>	dsolve(ode7, [separable]);

Opg 8

>	ode8:=(diff(y(x),x))=(x+1)/(y(x)+1);

>	odeadvisor(ode8);

>	ans8a:=dsolve({ode8, y(1)=-3});

>	simplify(%);

>	ans8b:=dsolve(ode8, implicit);

>	Int(x*sin(x^2),x=0..1/2*sqrt(Pi)) =int(x*sin(x^2),x=0..1/2*sqrt(Pi));

>	Int(x*sin(x^2),x) = int(x*sin(x^2),x);

>