Solve[2x+4==3,x]

Solve[{x+y==3,x-y==4},{x,y}]

Solve[{(x^2)-4==0},x]

sol=Solve[{x+(y^2)==2,(x^2)-(y^2)==0},{x,y}]

x+(y^2)/.sol[[3]]
(x^2)-(y^2)/.sol[[3]]

Solve[{(x^3)-8==0},x]

DSolve[D[y[x],x]==y[x],y[x],x]

DSolve[y'[x]==y[x],y[x],x]

sol=DSolve[{D[y[x],x]==y[x],y[0]==1},y[x],x]

y[x]

f=y[x]/.sol
f=y[x]/.sol[[1]]

Plot[f,{x,0,1}]

sol=NDSolve[{y''[t]==-0.1y'[t]-y[t]+BesselJ[0,5 t],y[0]==1,y'[0]==0},y[t],{t,0,200}]

Plot[y[t]/.sol[[1]],{t,30,40},PlotRange->All]

sol=DSolve[{(((y'[x]))^2)==y[x],y[0]==1},y[x],x]

f=y[x]/.sol
f=y[x]/.sol[[1]]

g=y[x]/.sol[[2]]

Plot[{f,g},{x,0,1}]

sol=DSolve[{vx'[t]==-ωc vy[t],vy'[t]==ωc vx[t],vz'[t]==0,vx[0]==vx0,vy[0]==vy0,vz[0]==vz0},{vx[t],vy[t],vz[t]},t]

sol=DSolve[{vx'[t]==-2 vy[t],vy'[t]==2 vx[t],vz'[t]==0,vx[0]==1,vy[0]==0,vz[0]==5},{vx[t],vy[t],vz[t]},t]

Plot[{vx[t]/.sol[[1]],vy[t]/.sol[[1]]},{t,0,20}]

ParametricPlot[{vx[t]/.sol[[1]],vy[t]/.sol[[1]]},{t,0,1}]

sol=DSolve[{x''[t]==-2 y'[t],y''[t]==2 x'[t],z''[t]==0,x[0]==0,y[0]==0,z[0]==0,x'[0]==1,y'[0]==0,z'[0]==0.5},{x[t],y[t],z[t]},t]

ParametricPlot3D[{x[t]/.sol[[1]],y[t]/.sol[[1]],z[t]/.sol[[1]]},{t,0,20}]