Misc 10 - Chapter 9 Class 12 Differential Equations
Last updated at April 16, 2024 by Teachoo
Solving Linear differential equations - Equation given
Ex 9.5, 19 (MCQ) Important
Misc 14 (MCQ) Important
Ex 9.5, 2
Ex 9.5, 10
Ex 9.5, 3 Important
Ex 9.5, 4
Misc 15 (MCQ)
Ex 9.5, 13
Ex 9.5, 8 Important
Misc 10 Important You are here
Misc 11
Ex 9.5, 14 Important
Ex 9.5, 6
Ex 9.5, 5 Important
Ex 9.5, 9
Ex 9.5, 7 Important
Ex 9.5, 15
Example 14
Ex 9.5, 1 Important
Ex 9.5, 12 Important
Ex 9.5, 11
Example 16
Example 17 Important
Example 22 Important
Solving Linear differential equations - Equation given
Last updated at April 16, 2024 by Teachoo
Misc 10 Solve the differential equation [š^(ā2āš„)/āš„āš¦/āš„] šš„/šš¦=1(š„ā 0)[š^(ā2āš„)/āš„āš¦/āš„] šš„/šš¦=1 š^(ā2āš„)/āš„ā š¦/āš„ =šš¦/šš„ š š/š š + š/āš = š^(āšāš)/āš Differential equation is of the form šš¦/šš„ + Py = Q where P = š/āš & Q = š^(āšāš)/āš IF. = eā«1ā"pdx" Finding ā«1āćš· š šć ā«1āćš· š š=ā«1āš š/āš ć ā«1āćš šš„=ā«1āćš„^((ā1)/2) šš„ć ć ā«1āćš šš„=ā«1āć(š„ (ā1)/2 + 1)/((ā1)/2 + 1) šš„ć ć ā«1āćš šš„=2š„^(1/2) ć= 2āš„ ā“ IF = š^(šāš) Solution is y (IF) = ā«1āć(šĆš¼š¹)šš„+šć yš^(šāš) = ā«1āć(š^(āšāš)/āšĆš^(šāš) )š š+šć yš^(2āš„) = ā«1āćšš„/āš„+šć yš^(2āš„) = ā«1āć1/āš„ šš„+šć yš^(2āš„) = ā«1āćš„^((ā1)/2) šš„+šć yš^(2āš„) = ā«1āć(š„^(ā1/2 + 1) )/(ā1/2 + 1)+šć "y" š^(2āš„) " = "2š„^(1/2) + C "y" š^(šāš) " = "2āš + C