69.1.36 problem 55

Internal problem ID [14189]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 55
Date solved : Tuesday, January 28, 2025 at 06:21:10 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 26

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

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

✓ Solution by Mathematica

Time used: 0.335 (sec). Leaf size: 27

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

\[ y(x)\to \frac {1}{2} e^{-c_1} \left (x^2-e^{2 c_1}\right ) \]