60.1.335 problem 336

Internal problem ID [10349]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 336
Date solved : Monday, January 27, 2025 at 07:18:32 PM
CAS classification : [_exact]

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

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 41

dsolve(((y(x)^2+1)^(1/2)+a*x)*diff(y(x),x)+(x^2+1)^(1/2)+a*y(x) = 0,y(x), singsol=all)
 

\[ \frac {x \sqrt {x^{2}+1}}{2}+\frac {\operatorname {arcsinh}\left (x \right )}{2}+a x y+\frac {y \sqrt {1+y^{2}}}{2}+\frac {\operatorname {arcsinh}\left (y\right )}{2}+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.224 (sec). Leaf size: 53

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

\[ \text {Solve}\left [a x y(x)+\frac {1}{2} \left (\text {arcsinh}(y(x))+y(x) \sqrt {y(x)^2+1}\right )+\frac {\text {arcsinh}(x)}{2}+\frac {1}{2} \sqrt {x^2+1} x=c_1,y(x)\right ] \]