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]
\[ \boxed {y \left (1+{y^{\prime }}^{2}\right )=2} \]
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 50
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 -\operatorname {csgn}\left (\cos \left (\textit {\_Z} \right )\right ) \cos \left (\textit {\_Z} \right )+c_{1} \right )\right )+1 \\ y \left (x \right ) &= \sin \left (\operatorname {RootOf}\left (-\textit {\_Z} -x +\operatorname {csgn}\left (\cos \left (\textit {\_Z} \right )\right ) \cos \left (\textit {\_Z} \right )+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*}