77.1.70 problem 90 (a)(page 123)

Internal problem ID [17960]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 90 (a)(page 123)
Date solved : Tuesday, January 28, 2025 at 11:18:30 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: 0.092 (sec). Leaf size: 20

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: 0.769 (sec). Leaf size: 38

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

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