Internal problem ID [2326]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 37, page 171
Problem number: 13.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y \left ({y^{\prime }}^{2}+1\right )=2} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 51
dsolve(y(x)*(1+diff(y(x),x)^2)=2,y(x), singsol=all)
\begin{align*} y \left (x \right ) = 2 y \left (x \right ) = -\sin \left (\operatorname {RootOf}\left (-\textit {\_Z} -x -\sqrt {\frac {\cos \left (2 \textit {\_Z} \right )}{2}+\frac {1}{2}}+c_{1} \right )\right )+1 y \left (x \right ) = \sin \left (\operatorname {RootOf}\left (-\textit {\_Z} -x +\sqrt {\frac {\cos \left (2 \textit {\_Z} \right )}{2}+\frac {1}{2}}+c_{1} \right )\right )+1 \end{align*}
✓ Solution by Mathematica
Time used: 0.359 (sec). Leaf size: 118
DSolve[y[x]*(1+y'[x]^2)==2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [-4 \arctan \left (\frac {\sqrt {\text {$\#$1}}}{\sqrt {2}-\sqrt {2-\text {$\#$1}}}\right )-\sqrt {-((\text {$\#$1}-2) \text {$\#$1})}\&\right ][-x+c_1] y(x)\to \text {InverseFunction}\left [-4 \arctan \left (\frac {\sqrt {\text {$\#$1}}}{\sqrt {2}-\sqrt {2-\text {$\#$1}}}\right )-\sqrt {-((\text {$\#$1}-2) \text {$\#$1})}\&\right ][x+c_1] y(x)\to 2 \end{align*}