29.37.29 problem 1152

Internal problem ID [5687]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 37
Problem number : 1152
Date solved : Monday, January 27, 2025 at 01:06:59 PM
CAS classification : [_Clairaut]

\begin{align*} y^{\prime } \ln \left (y^{\prime }+\sqrt {a +{y^{\prime }}^{2}}\right )-\sqrt {1+{y^{\prime }}^{2}}-x y^{\prime }+y&=0 \end{align*}

✗ 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: 60.045 (sec). Leaf size: 38

DSolve[D[y[x],x]*Log[D[y[x],x]+Sqrt[a+(D[y[x],x])^2]]-Sqrt[1+(D[y[x],x])^2]-x*D[y[x],x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -c_1 \log \left (\sqrt {a+c_1{}^2}+c_1\right )+c_1 x+\sqrt {1+c_1{}^2} \]