Differential equations

Question 1

Solving steps for differential equations

Answer 1

Integrate the equation containing the derivative
Include arbitrary constant c if necessary
Separate dy and dx using normal algebra rules eg division and multiplication to equate the x and y

Question 2

Newton’s law of cooling

Answer 2

dT/dt = -k(T - T₀)

Temperature (T)
Surrounding temperature (T₀)

Solve c by substituting a value into the equation, usually 0

Solve for k after solving for c

Obtain answer