> | with(DEtools):with(plots): |
30a
> | dsolve(diff(y(x),x$2)+y(x)=0); |
> | f:=(Ax+B)*exp(-x); |
> | diff(f,x$2)+f; |
> | f:=x*(A*cos(x)+B*sin(x)); |
> | ev:=diff(f,x$2)+f; |
> | simplify(ev); |
> |
30b
> | f:=exp(x)*((A*x^5+B*x^4+C*x^3+D*x^2+E*x+F)*sin(x)+(G*x^5+H*x^4+J*x^3+K*x^2+L*x+M)*cos(x)); |
> | ev:=diff(f,x$2)+f; |
> | col:=collect(expand(ev),{sin(x),cos(x),exp(x)}); |
> | p1:=collect([op([op(col)][1])][1],x); |
> | p2:=collect([op([op(col)][2])][1],x); |
31
> | de:=L*C*diff(v(t),t$2)+R*C*diff(v(t),t)+v(t)=cos(omega*t); |
> | dsolve(de); |
32
> | hom:=diff(y(x),x$2)+4*y(x)=0; |
> | dsolve(hom); |
> | y1:=sin(2*x); |
> | y2:=cos(2*x); |
> | g:=4*tan(2*x); |
> | y1p:=diff(y1,x); |
> | y2p:=diff(y2,x); |
> | u1p:=-y2*g/(y1*y2p-y2*y1p); |
> | u2p:=-y1*g/(y1*y2p-y2*y1p); |
> | u1p:=simplify(u1p); |
> | u2p:=simplify(u2p); |
> | int(u1p,x); |
> | u2p2:=2*(1/cos(2*x)-cos(2*x)); |
> | int(2/cos(2*x),x); |
> | int(2*cos(2*x),x); |