Internal problem ID [14675]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.5, page 175
Problem number: 67.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {2 y y^{\prime \prime }+y^{2}-{y^{\prime }}^{2}=0} \]
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 26
dsolve(2*y(t)*diff(y(t),t$2)+y(t)^2=diff(y(t),t)^2,y(t), singsol=all)
\begin{align*} y \left (t \right ) &= 0 \\ y \left (t \right ) &= \sqrt {c_{1}^{2}+c_{2}^{2}}+c_{1} \sin \left (t \right )+c_{2} \cos \left (t \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.254 (sec). Leaf size: 32
DSolve[2*y[t]*y''[t]+y[t]^2==y'[t]^2,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to c_2 \cos ^2\left (\frac {1}{2} (t-2 c_1)\right ) \\ y(t)\to c_2 \text {Interval}[\{0,1\}] \\ \end{align*}