Hey im having trouble in finishing this algo: A robot engine warms up with his trip and cooled down by a fan. The robot required to ensure that the engine is not overheating. Given that the temperature versus time engine is 1.2t=Tm Temperature of the enviroment is 15=Te Constant k=0.8 It i1s known that the rate of the cooling is define by dT/dt = -k(T-Te)+Tm Also known that the speed of the robot is 25m/s And the starting temparture of the engine is 35. We need to find the Differential Equations for the road founded in the last question for Each Δt=0.1 This is the answers that i dont know how to get to. temp is:

Time Temp[degC]
0.0 35.00
0.0 33.40
0.1 31.94
0.2 30.61
0.3 29.40
0.4 28.29
0.5 27.29
0.6 26.38
0.7 25.55
0.8 24.80
0.9 24.13
1.0 23.52

And when its getting warmer:

2.7 19.44
2.8 19.42
2.9 19.42
3.0 19.42
3.1 19.44
3.2 19.47
3.3 19.51
3.4 19.56
3.5 19.61
3.6 19.68
3.7 19.75

And the Path from the last question:

0 0
24 11
7 34
78 196
218 308
289 461
344 412
380 451
516 451
543 554
605 591
600 600

Thank you alot in advence!