Internal problem ID [3832]
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]
\[ \boxed {x^{2} \left (4 x -3 y\right ) y^{\prime }-\left (6 x^{2}-3 y x +2 y^{2}\right ) y=0} \]
✓ Solution by Maple
Time used: 0.078 (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: 0.119 (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]
\[ \text {Solve}\left [3 \arctan \left (\frac {y(x)}{x}\right )+2 \log \left (\frac {y(x)^2}{x^2}+1\right )-4 \log \left (\frac {y(x)}{x}\right )=-2 \log (x)+c_1,y(x)\right ] \]