75.8.21 problem 219

Internal problem ID [16837]
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
Date solved : Tuesday, January 28, 2025 at 09:34:26 AM
CAS classification : [_quadrature]

\begin{align*} y&=\arcsin \left (y^{\prime }\right )+\ln \left ({y^{\prime }}^{2}+1\right ) \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 31

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

\[ x -\int _{}^{y}\csc \left (\operatorname {RootOf}\left (-\textit {\_a} +\textit {\_Z} +\ln \left (2-\cos \left (\textit {\_Z} \right )^{2}\right )\right )\right )d \textit {\_a} -c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.359 (sec). Leaf size: 46

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

\[ \text {Solve}\left [\left \{x=2 \arctan (K[1])-\text {arctanh}\left (\sqrt {1-K[1]^2}\right )+c_1,y(x)=\arcsin (K[1])+\log \left (K[1]^2+1\right )\right \},\{y(x),K[1]\}\right ] \]