12.5.47 problem 46

Internal problem ID [1671]
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
Date solved : Monday, January 27, 2025 at 05:24:05 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Riccati]

\begin{align*} x^{3} y^{\prime }&=2 y^{2}+2 x^{2} y-2 x^{4} \end{align*}

✓ Solution by Maple

Time used: 0.005 (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)
 

\[ y = \tanh \left (-2 \ln \left (x \right )+2 c_1 \right ) x^{2} \]

✓ Solution by Mathematica

Time used: 0.913 (sec). Leaf size: 62

DSolve[x^3*D[y[x],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*}