15.18.20 problem 20

Internal problem ID [3263]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 35, page 157
Problem number : 20
Date solved : Monday, January 27, 2025 at 07:29:42 AM
CAS classification : [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]]

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 17

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

\[ y \left (x \right ) = \frac {\ln \left (2\right )}{2}+\frac {\ln \left (c_{1} x +c_{2} \right )}{2} \]

✓ Solution by Mathematica

Time used: 0.208 (sec). Leaf size: 21

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

\[ y(x)\to \frac {1}{2} \log (2 x-c_1)+c_2 \]