{y'(x) = -2 y, y(0)=1} from 0 to 2 by backward Euler - Wolfram|Alpha
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    link to /input/?i=0.0345716&lk=1&a=ClashPrefs_*Math-link to /input/?i=-0.016256&lk=1&a=ClashPrefs_*Math-
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    Method comparison:

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/input/?i=0.000268&lk=1&a=ClashPrefs_*Math-link to /input/?i=fourth%E2%80%90order+Runge%E2%80%90Kutta+method+%7By%27%5Bx%5D+%3D%3D+-2+y%5Bx%5D%2C+y%5B0%5D+%3D%3D+1%7D+from+0.+to+2.+stepsize+%3D+0.2&lk=1link to /input/?i=fourth%E2%80%90order+Runge%E2%80%90Kutta+method+%7By%27%5Bx%5D+%3D%3D+-2+y%5Bx%5D%2C+y%5B0%5D+%3D%3D+1%7D+from+0.+to+2.+stepsize+%3D+0.2&lk=1link to /input/?i=fourth%E2%80%90order+Runge%E2%80%90Kutta+method+%7By%27%5Bx%5D+%3D%3D+-2+y%5Bx%5D%2C+y%5B0%5D+%3D%3D+1%7D+from+0.+to+2.+stepsize+%3D+0.2&lk=1link to /input/?i=fourth%E2%80%90order+Runge%E2%80%90Kutta+method+%7By%27%5Bx%5D+%3D%3D+-2+y%5Bx%5D%2C+y%5B0%5D+%3D%3D+1%7D+from+0.+to+2.+stepsize+%3D+0.2&lk=1link to /input/?i=fourth%E2%80%90order+Runge%E2%80%90Kutta+method+%7By%27%5Bx%5D+%3D%3D+-2+y%5Bx%5D%2C+y%5B0%5D+%3D%3D+1%7D+from+0.+to+2.+stepsize+%3D+0.2&lk=1link to /input/?i=-0.0000219&lk=1&a=ClashPrefs_*Math-link to /input/?i=Runge%E2%80%90Kutta%E2%80%90Fehlberg+method+%7By%27%5Bx%5D+%3D%3D+-2+y%5Bx%5D%2C+y%5B0%5D+%3D%3D+1%7D+from+0.+to+2.+stepsize+%3D+0.2&lk=1link to /input/?i=Runge%E2%80%90Kutta%E2%80%90Fehlberg+method+%7By%27%5Bx%5D+%3D%3D+-2+y%5Bx%5D%2C+y%5B0%5D+%3D%3D+1%7D+from+0.+to+2.+stepsize+%3D+0.2&lk=1link to /input/?i=Runge%E2%80%90Kutta%E2%80%90Fehlberg+method+%7By%27%5Bx%5D+%3D%3D+-2+y%5Bx%5D%2C+y%5B0%5D+%3D%3D+1%7D+from+0.+to+2.+stepsize+%3D+0.2&lk=1link to /input/?i=Runge%E2%80%90Kutta%E2%80%90Fehlberg+method+%7By%27%5Bx%5D+%3D%3D+-2+y%5Bx%5D%2C+y%5B0%5D+%3D%3D+1%7D+from+0.+to+2.+stepsize+%3D+0.2&lk=1link to /input/?i=2.90%C3%9710%5E-8&lk=1&a=ClashPrefs_*Math-link to /input/?i=Bogacki%E2%80%90Shampine+method+%7By%27%5Bx%5D+%3D%3D+-2+y%5Bx%5D%2C+y%5B0%5D+%3D%3D+1%7D+from+0.+to+2.+stepsize+%3D+0.2&lk=1link to /input/?i=Bogacki%E2%80%90Shampine+method+%7By%27%5Bx%5D+%3D%3D+-2+y%5Bx%5D%2C+y%5B0%5D+%3D%3D+1%7D+from+0.+to+2.+stepsize+%3D+0.2&lk=1link to /input/?i=Bogacki%E2%80%90Shampine+method+%7By%27%5Bx%5D+%3D%3D+-2+y%5Bx%5D%2C+y%5B0%5D+%3D%3D+1%7D+from+0.+to+2.+stepsize+%3D+0.2&lk=1link to /input/?i=1.22%C3%9710%5E-8&lk=1&a=ClashPrefs_*Math-link to /input/?i=Dormand%E2%80%90Prince+method+%7By%27%5Bx%5D+%3D%3D+-2+y%5Bx%5D%2C+y%5B0%5D+%3D%3D+1%7D+from+0.+to+2.+stepsize+%3D+0.2&lk=1link to /input/?i=Dormand%E2%80%90Prince+method+%7By%27%5Bx%5D+%3D%3D+-2+y%5Bx%5D%2C+y%5B0%5D+%3D%3D+1%7D+from+0.+to+2.+stepsize+%3D+0.2&lk=1link to /input/?i=Dormand%E2%80%90Prince+method+%7By%27%5Bx%5D+%3D%3D+-2+y%5Bx%5D%2C+y%5B0%5D+%3D%3D+1%7D+from+0.+to+2.+stepsize+%3D+0.2&lk=1link to /input/?i=-1.24%C3%9710%5E-9&lk=1&a=ClashPrefs_*Math-link to /input/?i=backward+Euler+method+%7By%27%5Bx%5D+%3D%3D+-2+y%5Bx%5D%2C+y%5B0%5D+%3D%3D+1%7D+from+0.+to+2.+stepsize+%3D+0.2&lk=1link to /input/?i=backward+Euler+method+%7By%27%5Bx%5D+%3D%3D+-2+y%5Bx%5D%2C+y%5B0%5D+%3D%3D+1%7D+from+0.+to+2.+stepsize+%3D+0.2&lk=1link to /input/?i=backward+Euler+method+%7By%27%5Bx%5D+%3D%3D+-2+y%5Bx%5D%2C+y%5B0%5D+%3D%3D+1%7D+from+0.+to+2.+stepsize+%3D+0.2&lk=1link to /input/?i=-0.0163&lk=1&a=ClashPrefs_*Math-link to /input/?i=implicit+midpoint+method+%7By%27%5Bx%5D+%3D%3D+-2+y%5Bx%5D%2C+y%5B0%5D+%3D%3D+1%7D+from+0.+to+2.+stepsize+%3D+0.2&lk=1link to /input/?i=implicit+midpoint+method+%7By%27%5Bx%5D+%3D%3D+-2+y%5Bx%5D%2C+y%5B0%5D+%3D%3D+1%7D+from+0.+to+2.+stepsize+%3D+0.2&lk=1link to /input/?i=implicit+midpoint+method+%7By%27%5Bx%5D+%3D%3D+-2+y%5Bx%5D%2C+y%5B0%5D+%3D%3D+1%7D+from+0.+to+2.+stepsize+%3D+0.2&lk=1link to /input/?i=0.000974&lk=1&a=ClashPrefs_*Math-
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