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Question Number 169333 by Mastermind last updated on 28/Apr/22

S h o w t h a t i f y = C_{1} s i n x + C_{2} x t h e n

(1 + x c o t x) \frac{d^{2} y}{{d x}^{2}} - x \frac{d y}{d x} + y = 0

M a s t e r m i n d

Commented by som(math1967) last updated on 29/Apr/22

I t h i n k (1 + x c o t x) s h o u l d b e

(1 - x c o t x)

Commented by Mastermind last updated on 29/Apr/22

i f i t i s -, c o n t i n u e s o l v i n g i t

Commented by som(math1967) last updated on 29/Apr/22

y = C_{1} s i n x + C_{2} x

\frac{d y}{d x} = C_{1} c o s x + C_{2}

\frac{d^{2} y}{{d x}^{2}} = - C_{1} s i n x

n o w

(1 - x c o t x) \frac{d^{2} y}{{d x}^{2}} - x \frac{d y}{d x} + y

(1 - x \frac{c o s x}{s i n x}) (- C_{1} s i n x) - x (C_{1} c o s x + C_{2})

+ C_{1} s i n x + C_{2} x

= - C_{1} s i n x + C_{1} x c o s x - C_{1} x c o s x - {x C}_{2}

+ C_{1} s i n x + C_{2} x

= 0