29.21.6 problem 582

Internal problem ID [5176]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 21
Problem number : 582
Date solved : Monday, January 27, 2025 at 10:17:44 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class C`], _dAlembert]

\begin{align*} x^{2} \left (4 x -3 y\right ) y^{\prime }&=\left (6 x^{2}-3 y x +2 y^{2}\right ) y \end{align*}

✓ Solution by Maple

Time used: 0.144 (sec). Leaf size: 44

dsolve(x^2*(4*x-3*y(x))*diff(y(x),x) = (6*x^2-3*x*y(x)+2*y(x)^2)*y(x),y(x), singsol=all)
 

\[ 2 \ln \left (\frac {y \left (x \right )}{x}\right )-\ln \left (\frac {x^{2}+y \left (x \right )^{2}}{x^{2}}\right )-\frac {3 \arctan \left (\frac {y \left (x \right )}{x}\right )}{2}-\ln \left (x \right )-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.132 (sec). Leaf size: 43

DSolve[x^2(4 x-3 y[x])D[y[x],x]==(6 x^2-3 x y[x]+2 y[x]^2)y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [3 \arctan \left (\frac {y(x)}{x}\right )+2 \log \left (\frac {y(x)^2}{x^2}+1\right )-4 \log \left (\frac {y(x)}{x}\right )=-2 \log (x)+c_1,y(x)\right ] \]