83.35.1 problem 1

Internal problem ID [19421]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Misc. Exercise on chapter VII. Page 118
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 01:38:53 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

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

✓ Solution by Maple

Time used: 0.250 (sec). Leaf size: 25

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

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

✓ Solution by Mathematica

Time used: 60.032 (sec). Leaf size: 32

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

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