Internal problem ID [4343]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 37
Problem number: 1152.
ODE order: 1.
ODE degree: 0.
CAS Maple gives this as type [_Clairaut]
\[ \boxed {y^{\prime } \ln \left (y^{\prime }+\sqrt {a +{y^{\prime }}^{2}}\right )-\sqrt {1+{y^{\prime }}^{2}}-x y^{\prime }+y=0} \]
✗ Solution by Maple
dsolve(diff(y(x),x)*ln(diff(y(x),x)+sqrt(a+diff(y(x),x)^2))-sqrt(1+diff(y(x),x)^2)-x*diff(y(x),x)+y(x) = 0,y(x), singsol=all)
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 60.03 (sec). Leaf size: 38
DSolve[y'[x]*Log[y'[x]+Sqrt[a+(y'[x])^2]]-Sqrt[1+(y'[x])^2]-x*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -c_1 \log \left (\sqrt {a+c_1{}^2}+c_1\right )+c_1 x+\sqrt {1+c_1{}^2} \]