Moderate -0.3 This is a straightforward numerical methods question requiring Euler's method with given starting point and step size. It involves routine substitution into dy/dx = f(x,y) over two steps with basic arithmetic. While it requires careful calculation, it's a standard textbook exercise with no conceptual difficulty or problem-solving insight needed, making it slightly easier than average.
1 A curve passes through the point (1,3) and satisfies the differential equation
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { x } { 1 + x ^ { 3 } }$$
Starting at the point ( 1,3 ), use a step-by-step method with a step length of 0.1 to estimate the value of \(y\) at \(x = 1.2\). Give your answer to four decimal places.
1 A curve passes through the point (1,3) and satisfies the differential equation
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { x } { 1 + x ^ { 3 } }$$
Starting at the point ( 1,3 ), use a step-by-step method with a step length of 0.1 to estimate the value of $y$ at $x = 1.2$. Give your answer to four decimal places.
\hfill \mbox{\textit{AQA FP1 2013 Q1 [5]}}