Internal problem ID [9206]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1631 (6.41).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_potential_symmetries]]
\[ \boxed {y^{\prime \prime }-\left (3 y+f \left (x \right )\right ) y^{\prime }+y^{3}+y^{2} f \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 38
dsolve(diff(diff(y(x),x),x)-(3*y(x)+f(x))*diff(y(x),x)+y(x)^3+y(x)^2*f(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {-\left (\int c_{1} {\mathrm e}^{\int f \left (x \right )d x}d x \right )-c_{2}}{\int \left (\int c_{1} {\mathrm e}^{\int f \left (x \right )d x}d x \right )d x +c_{2} x +1} \]
✓ Solution by Mathematica
Time used: 0.046 (sec). Leaf size: 72
DSolve[f[x]*y[x]^2 + y[x]^3 - (f[x] + 3*y[x])*y'[x] + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\int _1^x\exp \left (\int _1^{K[2]}f(K[1])dK[1]\right ) c_1dK[2]+c_2}{\int _1^x\int _1^{K[5]}\exp \left (\int _1^{K[4]}f(K[3])dK[3]\right ) c_1dK[4]dK[5]+c_2 x+1} \\ \end{align*}