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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.

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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).

This problem has been solved

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