31.6.21 problem 21

Internal problem ID [5770]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 7
Problem number : 21
Date solved : Monday, January 27, 2025 at 01:16:12 PM
CAS classification : [_separable]

\begin{align*} \frac {y-x y^{\prime }}{y^{2}+y^{\prime }}&=\frac {y-x y^{\prime }}{1+x^{2} y^{\prime }} \end{align*}

✓ Solution by Maple

Time used: 0.076 (sec). Leaf size: 19

dsolve((y(x)-x*diff(y(x),x))/(y(x)^2+diff(y(x),x))=(y(x)-x*diff(y(x),x))/(1+x^2*diff(y(x),x)),y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= c_{1} x \\ y \left (x \right ) &= -\tanh \left (-\operatorname {arctanh}\left (x \right )+c_{1} \right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 60.137 (sec). Leaf size: 45

DSolve[(y[x]-x*D[y[x],x])/(y[x]^2+D[y[x],x])==(y[x]-x*D[y[x],x])/(1+x^2*D[y[x],x]),y[x],x,IncludeSingularSolutions -> True]
 

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