DSolve[y'[x]==2*x,y[x],x]

altmegold[c_]=Flatten[%]/.C[1]->c

DSolve[{y'[x]==2*x,y[2]==5},y[x],x]

partmegold=Flatten[%]

Plot[y[x]/.%,{x,-3,3}]

Plot[Evaluate[y[x]/.altmegold[c]/.{{c->1},{c->2},{c->3}}],{x,-2,2}]

intfv=DSolve[y'[x]-x*y[x]==x^3,y[x],x]

Plot[Evaluate[y[x]/.intfv/.{{C[1]->0},{C[1]->1},{C[1]->2}}],{x,-3,3}]

(*-----------------------*)
f[x_,y_]=y+x^2
Plot3D[f[x,y],{x,-2,2},{y,-2,2}]
Gradf={D[f[x,y],x],D[f[x,y],y]}
VectorPlot[Gradf,{x,-2,2},{y,-2,2}]
StreamPlot[Gradf,{x,-2,2},{y,-2,2}]

(*adott az f[x,y] gradiense*)
DSolve[{D[f[x, y], x]==2x y^3+y Cos[x y], 
                D[f[x,y],y]==3x^2y^2+x Cos[x y]},f[x,y],{x,y}]