Internal problem ID [10135]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1804 (book 6.213).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {2 \left (y-a \right ) \left (y-b \right ) \left (y-c \right ) y^{\prime \prime }-\left (\left (y-a \right )^{2} \left (y-b \right ) \left (y-c \right )+\left (y-b \right ) \left (y-c \right )\right ) {y^{\prime }}^{2}+\left (y-a \right )^{2} \left (y-b \right )^{2} \left (y-c \right )^{2} \left (A_{0} +\frac {B_{0}}{\left (y-a \right )^{2}}+\frac {C_{1}}{\left (y-b \right )^{2}}+\frac {D_{0}}{\left (y-c \right )^{2}}\right )=0} \]
✓ Solution by Maple
Time used: 0.343 (sec). Leaf size: 15344
dsolve(2*(y(x)-a)*(y(x)-b)*(y(x)-c)*diff(y(x),x$2)-( (y(x)-a)*(y(x)-b)*(y(x)-a)*(y(x)-c)+(y(x)-b)*(y(x)-c) )*diff(y(x),x)^2+( (y(x)-a)*(y(x)-b)*(y(x)-c) )^2*(A__0+B__0/(y(x)-a)^2+C__1/(y(x)-b)^2+D__0/(y(x)-c)^2)=0,y(x), singsol=all)
\begin{align*} \text {Expression too large to display} \text {Expression too large to display} \end{align*}
✓ Solution by Mathematica
Time used: 72.642 (sec). Leaf size: 3800
DSolve[2*(y[x]-a)*(y[x]-b)*(y[x]-c)*y''[x]-( (y[x]-a)*(y[x]-b)*(y[x]-a)*(y[x]-c)+(y[x]-b)*(y[x]-c) )*y'[x]^2+( (y[x]-a)*(y[x]-b)*(y[x]-c) )^2*(A0+B0/(y[x]-a)^2+C1/(y[x]-b)^2+D0/(y[x]-c)^2)==0,y[x],x,IncludeSingularSolutions -> True]
Too large to display