Question: Unit 3 VII -(Nonlinear Equations - Some Special Cases)ExercisesSolvex2d2ydx2(dydx)2=0Solveyd2ydx2(dydx)2=0SolutionsDependent variable y missing. u=dydx=>dudx=d2ydx2.x2d2ydx2(dydx)2=0=>x2dudxu2=0=>u=-x1c1x=dydxAnswer: y=1c12(1c1x-ln|1c1x|)c2.Independent.variable x is missing, by y is present. u=dydx=>dudx=d2ydx2.dudx=dudydydx=dudyu=d2ydx2.yd2ydx2(dydx)2=0=>y*ududyu2=0=>u=cy-1=dydx.Answer: y2=c1x-1c2

Unit 3 VII -(Nonlinear Equations - Some Special Cases)ExercisesSolvex2d2ydx2(dydx)2=0Solveyd2ydx2(dydx)2=0SolutionsDependent variable y missing. u=dydx=>dudx=d2ydx2.x2d2ydx2(dydx)2=0=>x2dudxu2=0=>u=-x1c1x=dydxAnswer: y=1c12(1c1x-ln|1c1x|)c2.Independent.variable x is missing, by y is present. u=dydx=>dudx=d2ydx2.dudx=dudy*dydx=dudy*u=d2ydx2.yd2ydx2(dydx)2=0=>y*ududyu2=0=>u=cy-1=dydx.Answer: y2=c1x-1c2

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