Lutasin ang d^2y/dx^2+9y=sec3x

$$\frac { d ^ { 2 } y } { d x ^ { 2 } } + 9 y = \sec 3 x$$

I-solve ang x (complex solution)

$$x=\frac{2\pi n_{1}}{3}-\frac{i\ln(\frac{-\sqrt{1-81y^{2}}+1}{9y})}{3}\text{, }n_{1}\in \mathrm{Z}$$

$$x=\frac{2\pi n_{2}}{3}+\frac{-i\ln(\frac{\sqrt{1-81y^{2}}+1}{y})+2i\ln(3)}{3}\text{, }n_{2}\in \mathrm{Z}\text{, }y\neq 0$$

I-solve ang y (complex solution)

$$y=\frac{1}{9\cos(3x)}$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }x=\frac{\pi n_{1}}{3}+\frac{\pi }{6}$$

I-solve ang y

$$y=\frac{1}{9\cos(x)\left(4\left(\cos(x)\right)^{2}-3\right)}$$

$$\exists n_{1}\in \mathrm{Z}\text{ : }\left(x>\frac{\pi n_{1}}{3}+\frac{\pi }{6}\text{ and }x<\frac{\pi n_{1}}{3}+\frac{\pi }{2}\right)$$