243 Days of KiyoRisu Stories

Day 12/243, Story 6, Chapter 2

Day 12/243, Story 6, Chapter 2

Continuation of that study fic. Is this even KiyoRisu anymore?

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Sudou strolled into the classroom.

"Ayanokouji! Are you here? I need your help!" Sudou shouted.

As usual, a pair of desks had been moved together towards the corner of the room. However, this time, Ayanokouji was reading a book, while Sakayanagi had her cheek placed on the desk next to him, sleeping.

Upon Sudou's arrival, Ayanokouji placed his index finger against his lip, communicating the current need for quiet.

Sudou bowed slightly as an apology before creeping towards the corner, trying to make as little noise as possible.

"Ayanokouji, can you help me?" Sudou asked, whispering.

Ayanokouji folded the corner of his page, creating a dog ear, before closing the book and putting it down. He turned towards Sudou.

"It depends. What do you need help with?"

"I have a homework sheet on... derivative equations?" Sudou replied, confused.

"Differential equations, Sudou-kun." corrected Ayanokouji.

"Ah yeah yeah, those."

"When is it due?"

"Ah, it's due tomorrow. But I figured that there was no way I was going to be able to get them done then, so I decided to do it today."

"How responsible of you, Sudou-kun."

Sudou looked at Ayanokouji sheepishly, scratching his cheek.

"Anyway... do you think you can help?"

Ayanokouji lifted his wrist and looked at his watch.

"It appears we have time, so I'll help."

"Great! Thanks man! I still owe you for last night." Sudou took a seat on the chair in front of Ayanokouji's desk before placing the sheet in front of him. Ayanokouji picked the piece of paper up and looked at the questions.

There were six in total. The text at the top read: 'Find the particular solutions for the following linear, homogeneous, second order differential equations, giving your answers in the form y = f(x).'

"Second order differential equations, huh?"

"Yeah, to be honest, I don't really know what any of the words mean." Sudou admitted, averting his eyes from the brown-haired boy.

"A second order differential equation is a differential equation which has exactly one independent variable, and any derivatives with respect to the independent variable have an order no greater than 2. For a linear second order differential equation, the equation can be written in this form."

Ayanokouji wrote the following on the corner of the sheet with a mechanical pencil:

y'' + p(x)y' + q(x)y=f(x)

He then placed his mechanical pencil down.

"For a homogeneous second order differential equation, the function f(x) will be equal to 0, which makes them easier to solve."

Sudou stared at Ayanokouji, wide-eyed.

"Um... to be honest, I don't really understand what you just said, but I'll just take your word for it. Can we look at the first question?"

"Very well."

Ayanokouji and Sudou leaned over the sheet and read the first part of the first question.