Solve this Differential equation. change in Temperature over the change in time dT/dt. (T) = Temperature | (t) = time

PLEASE SHOW ALL WORK!!!! (EVERY SINGLE STEP BY STEP BY STEP SHOW ALL SOUTIONS WHEN SOLVING THE DIFFERENTIAL EQUATION.)

Solve the Differential Equation Model.

Classify the Differential Equation as a Linear or a Non-linear.

Classify the Differential Equation as Autonomous or Non-Autonomous.

Classify the Differential Equation as Homogenous or Non- Homogenous.

Classify the Differential Equation as Partial Differential Equation (PDE) or Ordinary Differential Equation (ODE).

\fV =-COS(D3*PI()/4.42)*SIN(D3*PI()*0.5)-0.2*EXP(D3/20)/(D3*800-1) C D E F G H K T ( F ) t (min) AT At AT/At 40 0 -COS(D3*PI()/4.42)*SIN(D3*PI()*0.5)-0.2*EXP(D3/ 40 15 0 15 0 20)/(D3*800-1) 35 30 -5 15 -0.333333333 -0.842700778 dT/d 32 45 15 -0.2 -8.36915E-05 0.8 28 60 15 -0.266666667 -0.995194956 25 75 15 -0.2 -0.000250051 0.6 20 90 15 -0.333333333 -0.720 Vertical (Value) Axis Title 15 105 15 -0.333333333 -0.000840485 0.4 10o in i w ww in in w i is 12 120 15 -0.2 -0.136217337 CHANGE IN TEMPERATURE (AT) 0.2 9 135 15 -0.2 -0.003013429 5 150 15 0.266666667 0.502385184 0 0 165 15 -0.333333333 -0.011254361 50 8 180 15 0.533333333 0.910479487 -0.2 20 195 12 15 0.8 -0.043232999 -0.4 28 210 8 15 0.533333333 0.870349505 35 225 15 0.466666667 -0.169537124 0.6 38 240 | w 15 0.2 -0.425399538 40 260 N 20 0.1 Table 1: Temperature Readings over the Time of a Single Freeze-Thaw Cycle FigDependent Variable T Temperature (F) Independent Variable t Time [min] in Change in Temperature =T2-T1 At Change in Time =t2t1 Table 2: Variable Definition Changes in Temperature During a Temperature During a Freeze-Thaw Cycle Freeze-Thaw Cycle 45 1 1.5 dT/dt=-COS(t*PI()/4.42)*SIN(t*PI()*0.5)-0.2*EXP(t/20)/(t*800-1) 40 0.8 1 35 0.6 30 0.5 0.4 25 Temperature (T) CHANGE IN TEMPERATURE (AT) 0.2 O 20 150 200 250 300 0 15 150 200 250 300 -0.5 0.2 10 -1 -0.4 5 -0.6 -1.5 TIME (T) 0 50 100 150 200 250 300 (MINUTES) Time (t) (minutes) Figure 1: Change in Temperature over Time Figure 2: Temperature over Time\f