Internal problem ID [15081]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 7, Total differential equations. The integrating factor. Exercises page
61
Problem number: 193.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
\[ \boxed {-2 y^{3} x +3 y^{\prime } y^{2} x^{2}=-x^{4} \ln \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 84
dsolve(( x^4*ln(x)-2*x*y(x)^3)+(3*x^2*y(x)^2)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \left (-x^{2} \left (x \ln \left (x \right )-c_{1} -x \right )\right )^{\frac {1}{3}} \\ y \left (x \right ) &= -\frac {\left (-x^{2} \left (x \ln \left (x \right )-c_{1} -x \right )\right )^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{2} \\ y \left (x \right ) &= \frac {\left (-x^{2} \left (x \ln \left (x \right )-c_{1} -x \right )\right )^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.485 (sec). Leaf size: 77
DSolve[( x^4*Log[x]-2*x*y[x]^3)+(3*x^2*y[x]^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt [3]{x^2 (x+x (-\log (x))+c_1)} \\ y(x)\to -\sqrt [3]{-1} \sqrt [3]{x^2 (x+x (-\log (x))+c_1)} \\ y(x)\to (-1)^{2/3} \sqrt [3]{x^2 (x+x (-\log (x))+c_1)} \\ \end{align*}