Solve: xy' = y, when y(1) = 2. | Basic Mathematics 2081.2

Basic Mathematics2081.25 marksNumerical: differential equation solvingSeparable differential equations

Solve: $xy' = y$ , when $y(1) = 2$ . [5]

Solve: $xy' = y$, when $y(1) = 2$. [5]

Differential equation: $xy' = y$ - Initial condition: $y(1) = 2$ All required data is present. Step 1: Separate variables $x\frac{dy}{dx} = y$ $\frac{dy}{y} = \frac{dx}{x}$ Step 2: Integrate both sides $\int \frac{dy}{y} = \int \frac{dx}{x}$ $\lny = \lnx + C$ Step 3: General solution Ex...

Differential equation: $xy' = y$ - Initial condition: $y(1) = 2$ All required data is present. Step 1: Separate variables $$x\frac{dy}{dx} = y$$ $$\frac{dy}{y} = \frac{dx}{x}$$ Step 2: Integrate both sides $$\int \frac{dy}{y} = \int \frac{dx}{x}$$ $$\lny = \lnx + C$$ Step 3: General solution Ex...