81.3.27 problem 27

Internal problem ID [18645]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter III. Ordinary differential equations of the first order and first degree. Exercises at page 33
Problem number : 27
Date solved : Tuesday, January 28, 2025 at 12:07:28 PM
CAS classification : [_linear]

\begin{align*} \left (x^{2}-2 y x \right ) y^{\prime }+x^{2}-3 y x +2 y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 18

dsolve((x^2-2*x*y(x))*diff(y(x),x)+(x^2-3*x*y(x)+2*y(x)^2)=0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {x}{2} \\ y \left (x \right ) &= \left (-\ln \left (x \right )+c_{1} \right ) x \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 32

DSolve[(x^2-2*x*y[x])*D[y[x],x]+(x^2-3*x*y[x]+2*y[x]^2)==0,y[x],x,IncludeSingularSolutions -> True]
 

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