Solve the following differential equation: xfracdydx = x2 + 3y, x > 0. | Basic Mathematics 2078

Basic Mathematics20785 marksNumerical: solving differential equationLinear differential equations

Solve the following differential equation: $x\frac{dy}{dx} = x^2 + 3y$ , $x > 0$ . [5]

Solve the following differential equation: $x\frac{dy}{dx} = x^2 + 3y$, $x > 0$. [5]

Differential equation: $x\dfrac{dy}{dx} = x^2 + 3y$ - Domain: $x 0$ Divide by $x$ (valid since $x 0$ ): $\frac{dy}{dx} = x + \frac{3y}{x}$ $\frac{dy}{dx} - \frac{3}{x}y = x$ This is linear: $\dfrac{dy}{dx} + P(x)y = Q(x)$ with $P(x) = -\dfrac{3}{x}$ , $Q(x) = x$ . $$\mu(x) = e^{\int -\frac{3}{...

Differential equation: $x\dfrac{dy}{dx} = x^2 + 3y$ - Domain: $x 0$ Divide by $x$ (valid since $x 0$): $$\frac{dy}{dx} = x + \frac{3y}{x}$$ $$\frac{dy}{dx} - \frac{3}{x}y = x$$ This is linear: $\dfrac{dy}{dx} + P(x)y = Q(x)$ with $P(x) = -\dfrac{3}{x}$, $Q(x) = x$. $$\mu(x) = e^{\int -\frac{3}{...