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

$y=1+x-\dfrac12x^2+0x^3+\cdots$

Example of solution of differential equations

Example of solution of differential equations

Solution:

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