Find a particular solution of $y''+2y=10$ by using inspection.

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By inspection find a particular solution of $y''+2y=10$.

Write the answer in the form $a_nx^n+....+a_0$ with the highest degree order.

I'm not quite sure what "by inspection" means in this case. Any help would be much appreciated. Thank you.

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2 Answers

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Solving by inspection simply means you look at the problem, and try to come up with a solution through trial and error, using some logical thinking. In this case, setting $y = 5$ is a solution to the equation.

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Since the $RHS$ of $y''+2y=10$ is a constant, you try $y=C$ in your equation.

With $y=C$ we get $y'' =0$, thus $2C=10$ which implies $C=5$

So your particular solution by inspection is $y=5$

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