Internal problem ID [4332]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 37
Problem number: 1138.
ODE order: 1.
ODE degree: 0.
CAS Maple gives this as type [_Clairaut]
\[ \boxed {\left (1+{y^{\prime }}^{2}\right ) \sin \left (-y+x y^{\prime }\right )^{2}=1} \]
✓ Solution by Maple
Time used: 0.203 (sec). Leaf size: 139
dsolve((1+diff(y(x),x)^2)*sin(y(x)-x*diff(y(x),x))^2 = 1,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -x \sqrt {1-x}\, \sqrt {\frac {1}{x}}-\arcsin \left (\frac {1}{\sqrt {\frac {1}{x}}}\right ) y \left (x \right ) = x \sqrt {1-x}\, \sqrt {\frac {1}{x}}+\arcsin \left (\frac {1}{\sqrt {\frac {1}{x}}}\right ) y \left (x \right ) = -x \sqrt {x +1}\, \sqrt {-\frac {1}{x}}+\arcsin \left (\frac {1}{\sqrt {-\frac {1}{x}}}\right ) y \left (x \right ) = x \sqrt {x +1}\, \sqrt {-\frac {1}{x}}-\arcsin \left (\frac {1}{\sqrt {-\frac {1}{x}}}\right ) y \left (x \right ) = c_{1} x -\arcsin \left (\frac {1}{\sqrt {c_{1}^{2}+1}}\right ) y \left (x \right ) = c_{1} x +\arcsin \left (\frac {1}{\sqrt {c_{1}^{2}+1}}\right ) \end{align*}
✓ Solution by Mathematica
Time used: 0.335 (sec). Leaf size: 77
DSolve[(1+(y'[x])^2) (Sin[y[x]-x y'[x]])^2==1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x-\frac {1}{2} \arccos \left (\frac {-1+c_1{}^2}{1+c_1{}^2}\right ) y(x)\to \frac {1}{2} \arccos \left (\frac {-1+c_1{}^2}{1+c_1{}^2}\right )+c_1 x y(x)\to -\frac {\pi }{2} y(x)\to \frac {\pi }{2} \end{align*}