Internal problem ID [9368]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1790 (book 6.199).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [NONE]
Solve \begin {gather*} \boxed {-2 y \left (1-y\right ) y^{\prime \prime }+\left (1-3 y\right ) \left (y^{\prime }\right )^{2}-4 y y^{\prime } \left (f \relax (x ) y+g \relax (x )\right )+\left (1-y\right )^{3} \left (\mathit {f0} \relax (x )^{2} y^{2}-\mathit {f1} \relax (x )^{2}\right )+4 y^{2} \left (1-y\right ) \left (f \relax (x )^{2}-g \relax (x )^{2}-g^{\prime }\relax (x )-f^{\prime }\relax (x )\right )=0} \end {gather*}
✗ Solution by Maple
dsolve(-2*y(x)*(1-y(x))*diff(diff(y(x),x),x)+(1-3*y(x))*diff(y(x),x)^2-4*y(x)*diff(y(x),x)*(f(x)*y(x)+g(x))+(1-y(x))^3*(f0(x)^2*y(x)^2-f1(x)^2)+4*y(x)^2*(1-y(x))*(f(x)^2-g(x)^2-diff(g(x),x)-diff(f(x),x))=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(1 - y[x])^3*(-f1[x]^2 + f0[x]^2*y[x]^2) + 4*(1 - y[x])*y[x]^2*(f[x]^2 - g[x]^2 - Derivative[1][f][x] - Derivative[1][g][x]) - 4*y[x]*(g[x] + f[x]*y[x])*y'[x] + (1 - 3*y[x])*y'[x]^2 - 2*(1 - y[x])*y[x]*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved