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).

Question

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).

Knowee AI · Accepted Answer

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).

Obtain the general solution of the followingfirst order ODE :G ( ) F ,d t tdt =where F is a constant