77.1.71 problem 90 (b)(page 123)

Internal problem ID [17961]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 90 (b)(page 123)
Date solved : Tuesday, January 28, 2025 at 11:18:33 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} y^{\prime }&=-x -\sqrt {x^{2}+2 y} \end{align*}

✓ Solution by Maple

Time used: 0.099 (sec). Leaf size: 18

dsolve(diff(y(x),x)=-x-sqrt(x^2+2*y(x)),y(x), singsol=all)
 

\[ x +\sqrt {x^{2}+2 y}-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.924 (sec). Leaf size: 46

DSolve[D[y[x],x]==-x-Sqrt[x^2+2*y[x]],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {2 x-2 x \tanh \left (\frac {c_1}{2}\right )+2}{\left (-1+\tanh \left (\frac {c_1}{2}\right )\right ){}^2} \\ y(x)\to 0 \\ y(x)\to x+\frac {1}{2} \\ \end{align*}