(* 𝔏𝔦𝔟𝔬𝔯 𝔖𝔱𝔯𝔞𝔨𝔞 & ℨ𝔡𝔢𝔫𝔢𝔨 𝔑𝔬𝔳𝔞𝔨 *)

1+1*30

1/7
(1/7)

(((((2/3)/4)/2)/1)/5)

(2^(2^(2^2)))

(Sqrt[(Sqrt[6.])])
N[(Sqrt[(Sqrt[6])])]

cos=5;
cos(1+(10)+3+(2-1))
a=2;
aa=3;

Cos=5
N[Cos[10]]
Cos[10.]

Solve[5*(x^2)-15*x+3==0,x]

ClearAll[x]
Solve[x==10-3,x]

Solve[{2(x^2)+2y==4,6y+a*x==5},{x,y}]

2s
s2

C
I

Solve[Sin[x]==0,x]

FindRoot[Sin[x]==0,{x,3}]

DSolve[{y''[t]+4y'[t]==((Cos[t])^4),y[0]==0,y'[0]==1},y[t],t]

ClearAll[y]
y[0]==5

?*Laplace*

InverseLaplaceTransform[((p+1)/((p^3)+p+1)),p,t]//N

LaplaceTransform[(t^3)((Sin[2t])^2),t,s]

1+100!//N

Sin[5.]

5.//Sin

Sin@5.

N[Pi,50]

Pi//N[#,50]&

Integrate[Sin[(1/x)]*(x^15),x]
∫Sin[(1/x)]*(x^15)\[DifferentialD]x

(∑_(i=1)^Infinity)(1/(i^2))

∞(* esc + inf + esc *)

(* ==================== druhe cviceni ==================*)

DSolve[{x''[t]+2*x'[t]+2*x[t]==(E^(-t))+5*Sin[3*t],x[0]==3,x'[0]==-1},x[t],t]

Plot[(1/34) (E^(-t)) (80 Cos[t]+34 ((Cos[t])^2)-17 (E^t) Cos[t] Cos[2 t]+5 (E^t) Cos[t] Cos[4 t]+122 Sin[t]-34 (E^t) Cos[2 t] Sin[t]-20 (E^t) Cos[4 t] Sin[t]+34 ((Sin[t])^2)+34 (E^t) Cos[t] ((Sin[t])^2)-34 (E^t) Cos[t] Sin[2 t]+20 (E^t) Cos[t] Sin[4 t]+5 (E^t) Sin[t] Sin[4 t]),{t,0,3Pi}](*takhle NE!!!!!!!!!*)

{a,b,x,y}/.{a->3,b->2}(* komentar *)

{a,b,x,y}/.{a->3,a->11,a->15,b->2,c->10}

{a,b,x,y}/.{a->b,b->x,x->14}

x/.{{x->3},{x->1}}

ClearAll[t]

{{x->3},{x->1},{x->5}}[[1]]
{{x->3},{x->1},{x->5}}[[2]]
{{x->3},{x->1},{x->5}}[[0]]
{{x->3},{x->1},{x->5}}//TreeForm

x/.{{x->3},{x->1},{x->5}}

ClearAll[res1]

res1=x[t]/.DSolve[{x''[t]+2*x'[t]+2*x[t]==(E^(-t))+5*Sin[3*t],x[0]==3,x'[0]==-1},x[t],t][[1]];

x=debil;

?*Plot*

Plot[{res1,2*Cos[t]},{t,0,3Pi},AxesLabel->{"t [s]"," I [A]"},PlotLegends->{"řešení","2*cos(t)"},PlotLabel->"Nazev Grafu",PlotStyle->{{Green,Thick,DotDashed},{Blue,Thickness[0.05],Dashed}}]

Green
Thick
Dashed

Hue

Solve[{b*(y^2)+u==10*y,u==3y+u},{y,u}]

ClearAll[x,t]

x1=x[t]/.DSolve[{x''[t]+6*x'[t]+9*x[t]==(36*t-24)*(E^(-3*t))+18*t+18*Sin[3*t],x'[0]==64,x[0]==18},x[t],t][[1]];
x2=D[x1,t];

Plot[{x1,x2},{t,0,3π},PlotStyle->{{Red,Thick},{Orange,Thick,Dashed}},AxesLabel->{"t","x[t], x'[t]"},PlotLabel->"Graf"]