Internal problem ID [1024]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable
Equations. Section 2.4 Page 68
Problem number: 49.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(y)]`], _Riccati]
\[ \boxed {x \ln \left (x \right )^{2} y^{\prime }+4 \ln \left (x \right )^{2}-\ln \left (x \right ) y-y^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(x*(ln(x))^2*diff(y(x),x)=-4*(ln(x))^2+y(x)*ln(x)+y(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = 2 i \tan \left (2 i \ln \left (\ln \left (x \right )\right )+c_{1} \right ) \ln \left (x \right ) \]
✓ Solution by Mathematica
Time used: 1.04 (sec). Leaf size: 64
DSolve[x*(Log[x])^2*y'[x]==-4*(Log[x])^2+y[x]*Log[x]+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 i \log (x) \tan (2 i \log (\log (x))+c_1) \\ y(x)\to \frac {2 \log (x) \left (-\log ^4(x)+e^{2 i \text {Interval}[\{0,\pi \}]}\right )}{\log ^4(x)+e^{2 i \text {Interval}[\{0,\pi \}]}} \\ \end{align*}