Internal problem ID [15107]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 8. First order not solved for the derivative. Exercises page 67
Problem number: 219.
ODE order: 1.
ODE degree: 0.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y-\arcsin \left (y^{\prime }\right )-\ln \left ({y^{\prime }}^{2}+1\right )=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 31
dsolve(y(x)=arcsin(diff(y(x),x))+ln(1+diff(y(x),x)^2),y(x), singsol=all)
\[ x -\left (\int _{}^{y \left (x \right )}\csc \left (\operatorname {RootOf}\left (-\textit {\_a} +\textit {\_Z} +\ln \left (2-\cos \left (\textit {\_Z} \right )^{2}\right )\right )\right )d \textit {\_a} \right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.245 (sec). Leaf size: 46
DSolve[y[x]==ArcSin[y'[x]]+Log[1+y'[x]^2],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\left \{x=2 \arctan (K[1])-\text {arctanh}\left (\sqrt {1-K[1]^2}\right )+c_1,y(x)=\arcsin (K[1])+\log \left (K[1]^2+1\right )\right \},\{y(x),K[1]\}\right ] \]