Internal problem ID [15220]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 14. Differential equations admitting of
depression of their order. Exercises page 107
Problem number: 362.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {2 y y^{\prime \prime }-3 {y^{\prime }}^{2}-4 y^{2}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 22
dsolve(2*y(x)*diff(y(x),x$2)-3*diff(y(x),x)^2=4*y(x)^2,y(x), singsol=all)
\begin{align*} y &= 0 \\ y &= \frac {4}{\left (c_{2} \cos \left (x \right )-c_{1} \sin \left (x \right )\right )^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.637 (sec). Leaf size: 17
DSolve[2*y[x]*y''[x]-3*y'[x]^2==4*y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 \sec ^2(x+2 c_1) \]