Solve y′+2xy−1=0y' + 2xy - 1 = 0y′+2xy−1=0. | Mathematics I 2078

Mathematics I20785 marksNumerical: solving differential equationLinear equations

Solve y′+2xy−1=0y' + 2xy - 1 = 0y′+2xy−1=0. [5]

Given: - Differential equation: $y' + 2xy - 1 = 0$ No initial condition given, so we seek the general solution. --- $\frac{dy}{dx} + 2xy = 1$ This is a first-order linear ODE: $\frac{dy}{dx} + P(x)\,y = Q(x), \qquad P(x) = 2x, \quad Q(x) = 1$ $$\text{I.F.} = e^{\int P,dx} = e^{\int 2x,dx} =...

Given: - Differential equation: $y' + 2xy - 1 = 0$ No initial condition given, so we seek the general solution. --- $$\frac{dy}{dx} + 2xy = 1$$ This is a first-order linear ODE: $$\frac{dy}{dx} + P(x),y = Q(x), \qquad P(x) = 2x, \quad Q(x) = 1$$ $$\text{I.F.} = e^{\int P,dx} = e^{\int 2x,dx} =...

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