For the following questions, use a Maclaurin series (to the term in $x^3$) to approximate the solu

Question

For the following questions, use a Maclaurin series (to the term in $x^3$) to approximate the solution of the differential equations, using the initial conditions $\frac{\mathrm{d}y}{\mathrm{d}x} = y^2 - x$ given $y(0) = 1$ $\frac{\mathrm{d}y}{\mathrm{d}x} = y + xy^2$ given $y(0) = 2$ $\frac{\mathrm{d}^2y}{\mathrm{d}x^2} = xy$ given $y(0) = y'(0) = 1$

Accepted Answer

**(a)** $y\approx1+x+\frac{x^2}{2}+\frac{2x^3}{3}$. **(b)** $y\approx2+2x+3x^2+\frac{11x^3}{3}$. **(c)** $y\approx1+x+\frac{x^3}{6}$, near $x=0$.

Solution of Differential Equations using Maclaurin's series

Solution of Differential Equations using Maclaurin's series

Solution:

Solution locked