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Homework Statement:
 quadratic differential calculus
Relevant Equations:

4(y''y'')+(y'y')1=0
solve for y
suppose y''=r^2=s
y'=r
4(y''y'')(y'y')1=0=4(r^2)^2(r^2)1=4(s^2)s1
s=(b±√(b^24ac))/2a
s=(1±√17)/8
y=∫∫sdx=∫∫((1±√17)/8) dx=(1±√17)/8)(1/2)x^2+c1x+c2
y'=r
4(y''y'')(y'y')1=0=4(r^2)^2(r^2)1=4(s^2)s1
s=(b±√(b^24ac))/2a
s=(1±√17)/8
y=∫∫sdx=∫∫((1±√17)/8) dx=(1±√17)/8)(1/2)x^2+c1x+c2