Slide5.JPG

Slide6.JPG
Slide7.JPG


Transcript

Misc 15 The general solution of the differential equation 𝑒^𝑥 𝑑𝑦+(𝑦 𝑒^𝑥+2𝑥)𝑑𝑥=0 is (A) 𝑥 𝑒^𝑦+𝑥^2=𝐶 (B) 𝑥 𝑒^𝑦+𝑦^2=𝐶 (C) 𝑦 𝑒^𝑥+𝑥^2=𝐶 (D) 𝑦 𝑒^𝑦+𝑥^2=𝐶 Given equation 𝑒^𝑥 𝑑𝑦+(𝑦 𝑒^𝑥+2𝑥)𝑑𝑥=0 𝒆^𝒙 𝒅𝒚=−(𝒚 𝒆^𝒙+𝟐𝒙)𝒅𝒙 𝑑𝑦/𝑑𝑥= (−(𝑦𝑒^𝑥 + 2𝑥))/𝑒^𝑥 𝑑𝑦/𝑑𝑥 = (−𝑦𝑒^𝑥)/𝑒^𝑥 −2𝑥/𝑒^𝑥 𝑑𝑦/𝑑𝑥 = −𝑦−2𝑥/𝑒^𝑥 𝒅𝒚/𝒅𝒙 + y = (−𝟐𝒙)/𝒆^𝒙 Differential equation is of the form 𝑑𝑦/𝑑𝑥 + Py = Q where P = 1 & Q = (−𝟐𝒙)/𝒆^𝒙 Now, IF = 𝑒^∫1▒〖𝑃 𝑑𝑥〗 IF = 𝑒^∫1▒〖1 𝑑𝑥〗 IF = 𝒆^𝒙 Solution is y(IF) = ∫1▒〖(𝑄×𝐼𝐹)𝑑𝑥+𝑐〗 yex = ∫1▒〖(−𝟐𝒙)/𝒆^𝒙 𝒆^𝒙 𝒅𝒙+𝒄〗 yex = −∫1▒〖2𝑥 𝑑𝑥+𝑐〗 yex = −2×𝑥^2/2+𝑐 yex = −𝑥^2+𝑐 yex + 𝒙^𝟐=𝒄 So, the correct answer is (c)

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 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.