62.34.3 problem Ex 3

Internal problem ID [12995]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter IX, Miscellaneous methods for solving equations of higher order than first. Article 58. Independent variable absent. Page 135
Problem number : Ex 3
Date solved : Tuesday, January 28, 2025 at 04:46:36 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

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

✓ Solution by Maple

Time used: 1.273 (sec). Leaf size: 20

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

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

✓ Solution by Mathematica

Time used: 60.030 (sec). Leaf size: 30

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

\[ y(x)\to \log \left (-c_1 \text {sech}^2\left (\frac {1}{2} \sqrt {c_1 (x+c_2){}^2}\right )\right ) \]