Slide6.JPG

Slide7.JPG

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

Ex 9.5, 2 For each of the differential equation , find the𝑑𝑦/𝑑π‘₯+3𝑦=𝑒^(βˆ’2π‘₯) Step 1: Put in form 𝑑𝑦/𝑑π‘₯ + Py = Q π’…π’š/𝒅𝒙 + 3y = 𝒆^(βˆ’πŸπ’™) Step 2: Find P and Q by comparing, we get 𝑷=πŸ‘ and Q = 𝒆^(βˆ’πŸπ’™) Step 3 : Find Integrating factor, I.F. I.F. = 𝑒^∫1▒𝑝𝑑π‘₯ I.F. = 𝑒^∫1β–’3𝑑π‘₯ general solution : 𝑑𝑦/𝑑π‘₯+3𝑦=𝑒^(βˆ’2π‘₯) I.F. = 𝒆^πŸ‘π’™ Step 4 : Solution of the equation y Γ— I.F. = ∫1▒〖𝑄×𝐼.𝐹. 𝑑π‘₯+𝑐〗 Putting values y Γ— e3x = ∫1▒𝒆^(βˆ’πŸπ’™ + πŸ‘π’™) ,dx + 𝒄 ye3x = ∫1▒𝑒^(π‘₯ ) dx + 𝑐 ye3x = 𝑒^(π‘₯ ) dx + 𝑐 Dividing by 𝑒^(3π‘₯ ) y = e–2x + Ce–3x

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.