81.3.25 problem 25

Internal problem ID [18643]
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 : 25
Date solved : Tuesday, January 28, 2025 at 12:07:10 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.046 (sec). Leaf size: 55

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

\[ -\ln \left (\frac {-3 x^{2}+3 x y \left (x \right )+y \left (x \right )^{2}}{x^{2}}\right )-\frac {4 \sqrt {21}\, \operatorname {arctanh}\left (\frac {\left (2 y \left (x \right )+3 x \right ) \sqrt {21}}{21 x}\right )}{21}-\ln \left (x \right )-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.160 (sec). Leaf size: 68

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

\[ \text {Solve}\left [\frac {1}{21} \left (21-2 \sqrt {21}\right ) \log \left (-\frac {2 y(x)}{x}+\sqrt {21}-3\right )+\frac {1}{21} \left (21+2 \sqrt {21}\right ) \log \left (\frac {2 y(x)}{x}+\sqrt {21}+3\right )=-\log (x)+c_1,y(x)\right ] \]