15.18.26 problem 26

Internal problem ID [3269]
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 : 26
Date solved : Monday, January 27, 2025 at 07:29:50 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 24

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

\[ y \left (x \right ) = -x -\frac {\ln \left (2\right )}{2}+\frac {\ln \left (-{\mathrm e}^{4 x} c_{1} +c_{2} \right )}{2} \]

✓ Solution by Mathematica

Time used: 0.428 (sec). Leaf size: 52

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

\begin{align*} y(x)\to -\frac {1}{4} \log \left (e^{4 x}\right )+\frac {1}{2} \log \left (e^{4 x}+e^{2 c_1}\right )+c_2 \\ y(x)\to \frac {1}{4} \log \left (e^{4 x}\right )+c_2 \\ \end{align*}