15.7.10 problem 10

Internal problem ID [2991]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 11, page 45
Problem number : 10
Date solved : Monday, January 27, 2025 at 07:05:58 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 29

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: 7.031 (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 -i \\ y(x)\to i \\ \end{align*}