Obtain the general solution of the followingfirst order ODE :G ( ) F ,d t tdt =where F is a constant
Question
Obtain the general solution of the following first order ODE:
G(t) F(t), \frac{d}{dt} = 0
where F is a constant.
Solution
To obtain the general solution of the given first order ODE, we will follow these steps:
Step 1: Rewrite the ODE in standard form: G(t) dt/dt = F
Step 2: Separate the variables by moving all terms involving t to one side and all terms involving G(t) to the other side: dt = F/G(t) dt
Step 3: Integrate both sides of the equation with respect to t: ∫ dt = ∫ F/G(t) dt
Step 4: Evaluate the integrals: t = ∫ F/G(t) dt
Step 5: Solve the integral on the right-hand side to obtain the general solution. The specific form of the solution will depend on the function G(t).
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