For the following questions, use Euler's method to find the approximate value of $y$, using the gi

Question

For the following questions, use Euler's method to find the approximate value of $y$, using the given step size and initial conditions. $\frac{\mathrm{d}y}{\mathrm{d}x} = x^2 + y^2$ at $x = 0.4$ with step size $0.1$, given $y(0) = 1$. $\frac{\mathrm{d}y}{\mathrm{d}x} = 2xy$ at $x = 3$, with step size $0.4$, given $y(1) = 2$. $\frac{\mathrm{d}y}{\mathrm{d}x} = e^x + 2y^2$ at $x = 0.3$, with step size $0.1$, given $y(0) = 1$. $\frac{\mathrm{d}y}{\mathrm{d}x} = \sin(x + y) - e^x$ at $x = 0.5$, with step size $0.1$, given $y(0) = 4$.

Accepted Answer

(a) $1.57$; (b) $1.58$; (c) $2.48$; (d) $3.06$.

Numerical solutions of differential equations

Numerical solutions of differential equations