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Chapter 9 Class 12 Differential Equations (Term 2)

Serial order wise

Last updated at Aug. 20, 2021 by Teachoo

Misc 2 For each of the exercise given below , verify that the given function (šššššššš” šš šš„šššššš”) is a solution of the corresponding differential equation . (i) š„š¦=š š^š„+š š^(āš„)+š„^2 : š„ (š^2 š¦)/(šš„^2 )+2 šš¦/šš„āš„š¦+š„^2ā2=0 š„š¦=šš^š„+š š^(āš„)+š„^2 Differentiating w.r.t x (š(š„š¦))/šš„=š/šš„ [š š^š„+š š^(āš„)+š„^2 ] šš„/šš„ y+šš¦/šš„ š„ =šć šć^š„+(ā1)š š^(āš„)+2š„ y+y^ā² x =ać eć^xāb e^(āx)+2x Differentiating again w.r.t x š¦ā²+(š¦^ā² š„)^ā² =(šš^š„ )^ā²ā(šš^(āš„) )^ā²+(2š„)^ā² š¦^ā²+(š¦^ā²ā² š„+š¦^ā²Ć1)=šš^š„+šš^(āš„)+2 š¦^ā²ā² š„+2š¦^ā²=šš^š„+šš^(āš„)+2 Now, we know that š„š¦=šš^š„+š š^(āš„)+š„^2 š„š¦āš„^2=šš^š„+š š^(āš„) šš^š„+š š^(āš„)=š„š¦āš„^2 ...(1) (Given equation) ...(2) Putting (2) in (1) š¦^ā²ā² š„+2š¦^ā²=šš^š+šš^(āš)+2 š¦^ā²ā² š„+2š¦^ā²=ššāš^š+2 (š^2 š¦)/(šš„^2 ) š„+2 šš¦/šš„=ššāš^š+2 (š ^š š)/(š š^š ) š+š š š/š šāšš+š^š=š ā“ The given function is a solution