76.12.10 problem 16

Internal problem ID [17566]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.2 (Theory of second order linear homogeneous equations). Problems at page 226
Problem number : 16
Date solved : Tuesday, January 28, 2025 at 10:44:09 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.115 (sec). Leaf size: 33

dsolve(y(t)*diff(y(t),t$2)+diff(y(t),t)^2=0,y(t), singsol=all)
 

\begin{align*} y &= 0 \\ y &= \sqrt {2 c_{1} t +2 c_{2}} \\ y &= -\sqrt {2 c_{1} t +2 c_{2}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.160 (sec). Leaf size: 20

DSolve[y[t]*D[y[t],{t,2}]+D[y[t],t]^2==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to c_2 \sqrt {2 t-c_1} \]