rce=2y''[t]+3y'[t]+4y[t]==5*u[t]+6*u'[t];

laplrce=LaplaceTransform[rce,t,p]/.{ LaplaceTransform[y[t],t,p]->Y[p],LaplaceTransform[u[t],t,p]->U[p],y[0]->0,y'[0]->0,u[0]->0}

Solve[laplrce,Y[p]][[1]]

LaplaceTransform[y'[t],t,p]

DSolve[2y''[t]+3y'[t]-4y[t]==0,y[t],t]

2(λ^2)+3λ-4==0//Solve

pom=Y[p]*Together[(1/(p+3))-(1/(p+1))]
((Numerator[pom])/(Denominator[pom]//Expand))

Solve[Y==P1[p]*(U-P2[p]*(Yz-Y)),Y]

rce=3y'[t]+4y[t]==u[t];

laplrce=LaplaceTransform[rce,t,p]/.{ LaplaceTransform[y[t],t,p]->Y[p],LaplaceTransform[u[t],t,p]->U[p]}
Solve[laplrce,Y[p]]

rce={i'[t]==(1/L)*(u[t]-k*ω[t]-R*i[t]),ω'[t]==(1/J)*(k*i[t]-Mz[t])};
laplrce=LaplaceTransform[rce,t,p]/.{LaplaceTransform[i[t],t,p]->Ik[p],LaplaceTransform[Mz[t],t,p]->Mz[p],LaplaceTransform[u[t],t,p]->U[p],LaplaceTransform[ω[t],t,p]->ω[p],ω[0]->0,i[0]->0}

Solve[laplrce,ω[p],Ik[p]]

Solve[laplrce,{ω[p],Ik[p]}]