Internal problem ID [8386]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 49.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Abel]
\[ \boxed {y^{\prime }+a \phi ^{\prime }\left (x \right ) y^{3}+6 a \phi \left (x \right ) y^{2}+\frac {\left (1+2 a \right ) y \phi ^{\prime \prime }\left (x \right )}{\phi ^{\prime }\left (x \right )}=-2-2 a} \]
✗ Solution by Maple
dsolve(diff(y(x),x) + a*diff(phi(x),x)*y(x)^3 + 6*a*phi(x)*y(x)^2 +(2*a+1)*y(x)*diff(phi(x),x,x)/diff(phi(x),x) +2*(a+1)=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y'[x] + a*phi'[x]*y[x]^3 + 6*a*phi[x]*y[x]^2 +(2*a+1)*y[x]*phi''[x]/phi'[x] +2*(a+1)==0,y[x],x,IncludeSingularSolutions -> True]
Not solved