7.151 problem 1742 (book 6.151)

Internal problem ID [10064]

Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1742 (book 6.151).
ODE order: 2.
ODE degree: 1.

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

\[ \boxed {2 y^{\prime \prime } y-3 {y^{\prime }}^{2}-4 y^{2}=0} \]

✓ Solution by Maple

Time used: 0.031 (sec). Leaf size: 22

dsolve(2*diff(diff(y(x),x),x)*y(x)-3*diff(y(x),x)^2-4*y(x)^2=0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= \frac {4}{\left (c_{1} \sin \left (x \right )-c_{2} \cos \left (x \right )\right )^{2}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 1.076 (sec). Leaf size: 17

DSolve[-4*y[x]^2 - 3*y'[x]^2 + 2*y[x]*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

\[ y(x)\to c_2 \sec ^2(x+2 c_1) \]