35.8.21 problem 21

Internal problem ID [6228]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 13. Miscellaneous problems. page 466
Problem number : 21
Date solved : Monday, January 27, 2025 at 01:49:26 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 33

dsolve(diff(y(x),x)+x*y(x)=x/y(x),y(x), singsol=all)
 

\begin{align*} y &= \sqrt {{\mathrm e}^{-x^{2}} c_{1} +1} \\ y &= -\sqrt {{\mathrm e}^{-x^{2}} c_{1} +1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 1.932 (sec). Leaf size: 57

DSolve[D[y[x],x]+x*y[x]==x/y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt {1+e^{-x^2+2 c_1}} \\ y(x)\to \sqrt {1+e^{-x^2+2 c_1}} \\ y(x)\to -1 \\ y(x)\to 1 \\ \end{align*}