Does anyone know if wolfram alpha has step by step solutions for systems of differential equations? When I input them, it comes up with an answer but it does not give me the step by step solution. I would like it just for practicing purposes.
For example, I input the following into wolfram but it does not show me the step by step option as opposed to just inputting 1 linear ODE.
solve[{x' = -6x + 2y, y' = -20x + 6y}]Thanks
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$\begingroup$$$\begin{cases} x'=-6x+2y \\ y'=-20x+6y \end{cases}$$ One can solve it with matrix calculus or with the method of substitution (below) :
$2y=x'+6x \quad \to \quad 2y'=x''+6x'$
$$2y'=-40x+12y=-40x+6(x'+6x)=x''+6x'$$ $$x''+4x=0$$ $$x(t)=C_1\cos(2t)+C_2\sin(2t)$$ Then, you can compute $y(t)=\frac{1}{2}x'(t)+3x(t)$
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