Find the first four nonzero terms in each of two powers series solutions about the origin. Show that they form a fundamental set of solutions.
$y''+(\sin x)y=0$
what will be the solutions of the above differential equation????
[Math] $y”+(\sin x)y=0$ series solutions – differential equations
ordinary differential equations
Best Answer
The author means you need to expand $y$ in Taylor expansion and match up the terms $(x-x_{0})^{n}$ with each other. Here you may use $x_{0}=0$ for simplificity and matching $x^{n}$ terms. Mind that you need to expand $\sin[x]$ into $x-\frac{x^{3}}{3!}+O(x^{5})$, etc as well.