- #1

endykami

- 1

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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)-s-1

s=(-b±√(b^2-4ac))/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)-s-1

s=(-b±√(b^2-4ac))/2a

s=(1±√17)/8

y=∫∫sdx=∫∫((1±√17)/8) dx=(1±√17)/8)(1/2)x^2+c1x+c2