Use Maclaurin series to solve the differential equation \(\frac{\mathrm{d}y}{\mathrm{d}x} = x - y^2

Question

Use Maclaurin series to solve the differential equation $\frac{\mathrm{d}y}{\mathrm{d}x} = x - y^2 + 2$, where $y(0) = 1$, giving your answer up to and including the term in $x^3$.

Accepted Answer

$y = 1 + x - \frac{1}{2}x^2 + 0 \cdot x^3 + \dots $

Example of solution of differential equations

Example of solution of differential equations