Internal problem ID [1021]
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: 46.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Riccati]
Solve \begin {gather*} \boxed {y^{\prime } x^{3}-2 y^{2}-2 y x^{2}+2 x^{4}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 17
dsolve(x^3*diff(y(x),x)=2*(y(x)^2+x^2*y(x)-x^4),y(x), singsol=all)
\[ y \relax (x ) = \tanh \left (-2 \ln \relax (x )+2 c_{1}\right ) x^{2} \]
✓ Solution by Mathematica
Time used: 0.507 (sec). Leaf size: 62
DSolve[x^3*y'[x]==2*(y[x]^2+x^2*y[x]-x^4),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to i x^2 \tan (2 i \log (x)+c_1) \\ y(x)\to \frac {x^2 \left (-x^4+e^{2 i \text {Interval}[\{0,\pi \}]}\right )}{x^4+e^{2 i \text {Interval}[\{0,\pi \}]}} \\ \end{align*}