Question

Solve y"+ (cos x) y= 0 .​

Answer 1

Answer:

y=∑n=0∞ann!xn

y′=∑n=1∞an(n−1)!xn−1=∑n=0∞an+1n!xn

y′′=∑n=2∞an(n−2)!xn−2=∑n=0∞an+2n!xn

y′′−2y′+y=0

∑n=0∞(an+2n!xn−2an+1n!xn+ann!xn)=0

∑n=0∞(an+2−2an+1+an)xnn!=0

an+2−2an+1+an=0

an+2=2an+1−an

a0=a0,a1=a1

a2=2a1−a0

a3=2(2a1−a0)−a1=3a1−2a0

a4=2(3a1−2a0)−(2a1−a0)=4a1−3a0

⋯

an=na1−(n−1)a0=a0+n(a1−a0)

y=∑n=0∞ann!xn=∑n=0∞a0+n(a1−a0)n!xn=∑n=0∞a0n!xn+∑n=1∞(a1−a0)(n−1)!xn=a0∑n=0∞xnn!+(a1−a0)∑n=0∞xn+1n!=a0∑n=0∞xnn!+(a1−a0)x∑n=0∞xnn!  

y=c1ex+c2xex

Step-by-step explanation:

please mark me as brainliest

Answer 2

Answer:

bxvdgd djdvfc rgcxxt hhd the he d fus. c down be hr rghr r the d tgrbd f thbd d dvhfr. dvdjd f