1. **State the problem:** Solve the differential equation with the initial condition $y(0)=0$. 2. **Identify the differential equation:** Since the user did not specify the equation, let's assume a common example: $$\frac{dy}{dx} = y$$ with initial condition $y(0)=0$. 3. **General solution:** The differential equation $$\frac{dy}{dx} = y$$ is separable. We use the formula for separable equations: $$\frac{dy}{y} = dx$$ 4. **Integrate both sides:** $$\int \frac{1}{y} dy = \int 1 dx$$ $$\ln|y| = x + C$$ 5. **Solve for $y$:** $$|y| = e^{x+C} = e^C e^x$$ Let $A = e^C$, so $$y = A e^x$$ 6. **Apply initial condition $y(0)=0$:** $$y(0) = A e^0 = A = 0$$ 7. **Final solution:** Since $A=0$, the solution is $$y = 0$$ This means the only solution satisfying the initial condition is the trivial solution $y=0$. If you have a different differential equation, please provide it for a specific solution.