Sentence examples for using the second equation from inspiring English sources

Using the second equation of (1.1) and Young's inequality, we have (4.17).

In the same way, using the second equation of (13), the second equation of system (7) can be constructed.

Substituting this into Δ y n = Δ ( c n ( Δ x n ) γ ). and using the second equation of (S) we get Equation (R2).

Using the second equation of (2), we obtain exp bigl y(t) bigr)leqexp bigl y(0) bigr)exp biggl( int_{0}^{t} biggl -d(t)+frac{f(t)}{biggl -d} biggr) Delta s biggr).

Using the second equation in system (2) and taking the integral of that equation from 0 to t, we obtain exp bigl y(t) bigr)= exp bigl y(0) bigr)exp biggl( int_{0}^{t} -d(s)+frac{f(s)exp (x s))}{alpha(s)+beta(s) exp (x s))+ m(s)exp (y(s))} Delta s biggr).

Using the second equation of model (1.2), we obtain begin{aligned} &frac{partial v}{ partial t}leq- -Delta)^{alpha} v+r(1-v/K)vquad mbox{in } (0,t}leq- -Delta, &frac{part}leq- -Deltaalnu}=0quadmbox{on } (0,T) times partialOmega, &v(0,x)=v_{0}(x)quadmbox{in } Omega.

Accordingly, using the fourth equation, we calculate the percentage change value to be 264%.

Using the first equation of (1.1), we can easily check that (4.15).

Using the first equation of system (5.1) and Harnack's inequality, we obtain (max_{overline{Omega}}u_{m}leq A_{2}min_{overline{Omega}}u_{m} ).

Notice, if ȳ = 0, then using the first equation of System (37 we obtain α 1 = 0 which is impossible.

Next, we couple to a linear equation of the form where are first degree in, and using the first equation we eliminate.