4.36.5 y(x)(a+bx+cx2)2+Ay(x)=0

ODE
y(x)(a+bx+cx2)2+Ay(x)=0 ODE Classification

[[_Emden, _Fowler]]

Book solution method
TO DO

Mathematica
cpu = 1.46083 (sec), leaf count = 199

{{y(x)a+x(b+cx)exp(4acb214Ab24actan1(b+2cx4acb2)b24ac)(c1exp(24acb214Ab24actan1(b+2cx4acb2)b24ac)+c2b24ac14Ab24ac)}}

Maple
cpu = 0.148 (sec), leaf count = 178

{y(x)=cx2+bx+a((1(i4acb22cxb)(2cx+b+i4acb2)1)c24ac+b24Ac214ac+b2_C2+(1(i4acb22cxb)(2cx+b+i4acb2)1)c24ac+b24Ac214ac+b2_C1)} Mathematica raw input

DSolve[A*y[x] + (a + b*x + c*x^2)^2*y''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> (Sqrt[a + x*(b + c*x)]*(E^((2*Sqrt[-b^2 + 4*a*c]*Sqrt[1 - (4*A)/(b^2 -
 4*a*c)]*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/Sqrt[b^2 - 4*a*c])*C[1] + C[2]/
(Sqrt[b^2 - 4*a*c]*Sqrt[1 - (4*A)/(b^2 - 4*a*c)])))/E^((Sqrt[-b^2 + 4*a*c]*Sqrt[
1 - (4*A)/(b^2 - 4*a*c)]*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/Sqrt[b^2 - 4*a*
c])}}

Maple raw input

dsolve((c*x^2+b*x+a)^2*diff(diff(y(x),x),x)+A*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = (c*x^2+b*x+a)^(1/2)*(((I*(4*a*c-b^2)^(1/2)-2*c*x-b)/(2*c*x+b+I*(4*a*c-b^2
)^(1/2)))^(-1/2*c/(-4*a*c+b^2)^(1/2)*((-4*a*c+b^2-4*A)/c^2)^(1/2))*_C2+((I*(4*a*
c-b^2)^(1/2)-2*c*x-b)/(2*c*x+b+I*(4*a*c-b^2)^(1/2)))^(1/2*c/(-4*a*c+b^2)^(1/2)*(
(-4*a*c+b^2-4*A)/c^2)^(1/2))*_C1)