Problem

$\left\{\begin{array}{l}\frac{d y}{d x}=y \\ V(0)=3\end{array}\right.$

Solution

Step 1 :Given the first-order differential equation and initial condition: \(\left\{\begin{array}{l}\frac{d y}{d x}=y \\ V(0)=3\end{array}\right.\)

Step 2 :Find the general solution to the differential equation: \(y(x) = C_1 e^x\)

Step 3 :Apply the initial condition V(0) = 3: \(y(0) = C_1 e^0\)

Step 4 :Solve for \(C_1\): \(C_1 = 3\)

Step 5 :Substitute \(C_1\) back into the general solution: \(\boxed{y(x) = 3e^x}\)

From Solvely APP
Source: https://solvelyapp.com/problems/16344/

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