1st-Order Differential Equation Solver

$\displaystyle {\frac{dy}{dx}}=f(x,y)$ or $\displaystyle {y'}=f(x,y)$ type first-order differential equations are solved using a numerical analysis method. Use the variables $x$ and $y$. You may use the mathematical operators +, −, *, / and the functions listed below. To compute powers, use the pow function. For example, instead of writing $x^2$, write pow(x,2).

Differential equation to be solved: $\displaystyle {\frac{dy}{dx}}=f(x,y)=$

Numerical Method:

Show intermediate results
Show only the final result

Required boundary (initial) conditions:

$x_0=$

$y_0=$

The desired $x$ value: $x_n=$

Step size $\Delta x=$

Functions that can be used inside the equation:
$\begin{array}{lll|lll} x^a & \Rightarrow & \mathrm{pow(x,a)} \\\sin\, x & \Rightarrow & \mathrm{sin(x)} &\cos\,x & \Rightarrow & \mathrm{cos(x)} \\\tan\,x & \Rightarrow &\mathrm{tan(x)} &\ln\,x & \Rightarrow & \mathrm{log(x)} \\e^x & \Rightarrow & \mathrm{exp(x)} &\left|x\right| & \Rightarrow & \mathrm{abs(x)} \\\arcsin\,x & \Rightarrow & \mathrm{asin(x)} &\arccos\,x & \Rightarrow & \mathrm{acos(x)} \\\arctan\,x & \Rightarrow & \mathrm{atan(x)} &\sqrt{x} & \Rightarrow & \mathrm{sqrt(x)} \\ \\\pi & \Rightarrow & \mathrm{pi} &e \mathrm{ number} & \Rightarrow & \mathrm{esay} \\\ln\,2 & \Rightarrow &\mathrm{LN2} & \ln\,10 & \Rightarrow & \mathrm{LN10} \\\log_{2}\,e & \Rightarrow & \mathrm{Log2e} & \log_{10}\,e & \Rightarrow & \mathrm{Log10e} \end{array}$

Use a dot (.) as the decimal separator. For example, write 1.0 instead of 1,0.

Example: Let us solve the following differential equation:
$ \begin{matrix} \displaystyle\frac{\mathrm{d} y}{\mathrm{d} x}=y-2x+e^x \end{matrix}$

In the equation box, write:
$\displaystyle\frac{\mathrm{d} y}{\mathrm{d} x}$: y-2*x+pow(esay,x)
Enter the boundary values in the appropriate boxes. For example, with $x_0=1.0$ and $y_0=-1.2$, the corresponding $y_n$ value for the requested $x_n$ is displayed—along with the calculation steps—when you click "Calculate".

NOTE: Writing x^2 is not supported; use pow(x,2) instead.