78.7.11 problem 3 (a)

Internal problem ID [18197]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 11 (Reduction of order). Problems at page 87
Problem number : 3 (a)
Date solved : Tuesday, January 28, 2025 at 11:37:48 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 1.777 (sec). Leaf size: 16

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

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