Solution Of Differential Equations

Step 1: Use the given point to find . We are given that the curve passes through the point , so substitute and into the equation: Since , this simplifies to: Conclusion: The equation of the curve is:

Step 1: Rearrange the equation to separate variables.
Rearrange the equation to separate the variables and :

Step 2: Integrate both sides.
Now, integrate both sides: On the left-hand side, the integral of is: On the right-hand side, the integral of is:

Step 3: Include the constant of integration.
Equating the results of the integrals and adding the constant of integration on the right-hand side: Conclusion: The general solution is:

Step 1: Write the differential equation.

Step 2: Separate variables.

Step 3: Integrate both sides.
So,

Step 4: Use initial condition.
Point lies on the curve. Substitute:

Step 5: Final equation of curve.

Final Answer: