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I want to find exact solution of a nonlinear ode with its boundary conditions . the equation

and its b.cs are written below :

a*y''''+y''' y -y'' y' = 0 y(h/2)=V1 , y(-h/2)=V2 , y'(h/2)=0 , y'(-h/2)=0

where V1 , V2 , a and h are constant .

although with integerating from above equation , the order of ode reduce to 3 but the problem is until unsolveable .

after integrating from above equation we have : a y''' +y'' y -y'^2 =C

where C is constant .

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# Solving forth order nonlinear ode

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