15.18.13 problem 13

Internal problem ID [3256]
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 : 13
Date solved : Monday, January 27, 2025 at 07:28:55 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} y^{\prime \prime }&=1+{y^{\prime }}^{2} \end{align*}

✓ Solution by Maple

Time used: 0.036 (sec). Leaf size: 17

dsolve(diff(y(x),x$2)=1+diff(y(x),x)^2,y(x), singsol=all)
 

\[ y \left (x \right ) = -\ln \left (c_{1} \sin \left (x \right )-c_2 \cos \left (x \right )\right ) \]

✓ Solution by Mathematica

Time used: 1.969 (sec). Leaf size: 16

DSolve[D[y[x],{x,2}]==1+D[y[x],x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2-\log (\cos (x+c_1)) \]