Find the initial value problem in fracdydx + 2y = 3, y(0) = 1. | Basic Mathematics 2077

Basic Mathematics20775 marksNumerical: initial value problem ODEInitial value problems

Find the initial value problem in $\frac{dy}{dx} + 2y = 3$ , $y(0) = 1$ . [5]

Find the initial value problem in $\frac{dy}{dx} + 2y = 3$, $y(0) = 1$. [5]

Differential equation: $\dfrac{dy}{dx} + 2y = 3$ - Initial condition: $y(0) = 1$ All required data is present. Identify form: First-order linear ODE $\frac{dy}{dx} + P(x)y = Q(x), \quad P(x) = 2, \quad Q(x) = 3$ Integrating factor: $\mu(x) = e^{\int 2\,dx} = e^{2x}$ Multiply through by

Differential equation: $\dfrac{dy}{dx} + 2y = 3$ - Initial condition: $y(0) = 1$ All required data is present. Identify form: First-order linear ODE $$\frac{dy}{dx} + P(x)y = Q(x), \quad P(x) = 2, \quad Q(x) = 3$$ Integrating factor: $$\mu(x) = e^{\int 2,dx} = e^{2x}$$ Multiply through by