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Misc 9 - Chapter 9 Class 12 Differential Equations

Last updated at May 29, 2023 by

Misc 11 - Find particular solution: (x - y) (dx + dy) = dx - dy - Solving homogeneous differential equation

Misc 11 - Chapter 9 Class 12 Differential Equations - Part 2
Misc 11 - Chapter 9 Class 12 Differential Equations - Part 3 Misc 11 - Chapter 9 Class 12 Differential Equations - Part 4

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Misc 9 Find a particular solution of the differential equation ( )( + )= , given that = 1 , when =0 ( : = ) ( )( + )= + y dx y dy = dx dy x dx y dx dx = xdy + y dy dy (x y 1) dx = ( x + y 1)dy / = ( 1)/( + 1) / = (( 1))/( ( + 1)) Put x y = t Diff w.r.t.x 1 / = / Putting value of t & dt in (1) 1 / = (( 1))/( + 1) / = 1 + (( 1))/( + 1) / = ( + 1 + 1)/( + 1) / = 2 /( 1) ( 1)/2 dt = Integrating both sides 1 ( + 1 )/2 = 1 1 ( /2 +1/2 ) = x + c 1 (1/2+1/2 ) = x + c /2 + 1/2 log | | = x + c Putting value of t = x y ( )/2 + 1/2 log | | = x + C Given y = 1 when x = 0 Put x = 0 & y = 1 in (2) (0 + 1)/2 + 1/2 log 1 = 0 + C 1/2 = C C = 1/2 Putting value in (2) ( )/2+1/2 log | |= +1/2 ( )/2+1/2 log | |=(2 + 1)/2 x y + log | |=2 +1 log | | = 2x + 1 x + y log | | = x + y + 1

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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.