7.153 problem 1744 (book 6.153)

Internal problem ID [9318]

Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1744 (book 6.153).
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _missing_x]]

\[ \boxed {2 y^{\prime \prime } y-6 {y^{\prime }}^{2}+\left (1+y^{3} a \right ) y^{2}=0} \]

Solution by Maple

Time used: 0.063 (sec). Leaf size: 75

dsolve(2*diff(diff(y(x),x),x)*y(x)-6*diff(y(x),x)^2+(1+a*y(x)^3)*y(x)^2=0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) = 0 \\ \int _{}^{y \left (x \right )}-\frac {2}{\sqrt {4 c_{1} \textit {\_a}^{4}+4 \textit {\_a}^{3} a +1}\, \textit {\_a}}d \textit {\_a} -x -c_{2} = 0 \\ \int _{}^{y \left (x \right )}\frac {2}{\sqrt {4 c_{1} \textit {\_a}^{4}+4 \textit {\_a}^{3} a +1}\, \textit {\_a}}d \textit {\_a} -x -c_{2} = 0 \\ \end{align*}

Solution by Mathematica

Time used: 17.853 (sec). Leaf size: 2761

DSolve[y[x]^2*(1 + a*y[x]^3) - 6*y'[x]^2 + 2*y[x]*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

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