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  "body": "\n## Summary\n\nThe shooting method solves a [[boundary value problem|TM8VQJWGHZ]] by solving a family of [[initial value problems|0FXDW992DS]] instead.\nOne guesses the missing initial data, solves forward, and adjusts the guess until the condition at the far end holds.\nThis turns the boundary value problem into a root-finding problem for a function of the missing initial data.\nIt is used both as a numerical method and as a tool in existence proofs.\n\n## Explanations\n\n### L1 human\n\nThink of firing a cannon at a target on a hill.\nYou know where the cannon stands but not the right angle.\nYou fire, see whether the ball lands too short or too far, and correct the angle.\nFor $y'' = -y$, $y(0) = 0$, $y(\\pi/2) = 1$, one shoots with $y'(0) = s$ and gets $y = s \\sin x$.\nThe ball hits the target $y(\\pi/2) = 1$ exactly when $s = 1$.\n",
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