69.1.37 problem 56

Internal problem ID [14190]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 56
Date solved : Tuesday, January 28, 2025 at 06:21:16 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.193 (sec). Leaf size: 27

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

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

✓ Solution by Mathematica

Time used: 0.245 (sec). Leaf size: 57

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

\begin{align*} y(x)\to -e^{\frac {c_1}{2}} \sqrt {2 x+e^{c_1}} \\ y(x)\to e^{\frac {c_1}{2}} \sqrt {2 x+e^{c_1}} \\ y(x)\to 0 \\ \end{align*}