Practice Ordinary Differential Equations - CSIR-UGC NET Offered by Unacademy

Ordinary Differential Equations

Consider a function in the range $0 \leq x \leq \pi$ . Find the half-range Fourier cosine series.

$\frac{3 \pi}{2}-\frac{12}{\pi}$ $\left[\cos x+\frac{1}{9} \cos 3 x+\frac{1}{25} \cos 5 x+\ldots .\right]$

$\frac{3 \pi}{2}+\frac{12}{\pi}$ $\left[\cos x+\frac{1}{9} \cos 3 x+\frac{1}{25} \cos 5 x+\ldots \ldots\right]$

$\frac{\pi}{2}+\frac{12}{\pi}$ $\left[\cos x+\frac{1}{9} \cos 3 x+\frac{1}{25} \cos 5 x+\ldots \ldots\right]$

$\frac{\pi}{2}-\frac{6}{\pi}$ $\left[\cos x+\frac{1}{9} \cos 3 x+\frac{1}{25} \cos 5 x+\ldots .\right]$