21.6 problem 582

Internal problem ID [3324]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 21
Problem number: 582.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class C], _dAlembert]

Solve \begin {gather*} \boxed {x^{2} \left (4 x -3 y\right ) y^{\prime }-\left (6 x^{2}-3 y x +2 y^{2}\right ) y=0} \end {gather*}

Solution by Maple

Time used: 0.047 (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)
 

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

Solution by Mathematica

Time used: 0.107 (sec). Leaf size: 43

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

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