28.1.43 problem 44

Internal problem ID [4349]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 44
Date solved : Monday, January 27, 2025 at 09:07:42 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{2}-\left (y x +x^{3}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.074 (sec). Leaf size: 35

dsolve((y(x)^2)-(x*y(x)+x^3)*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \left (-x -\sqrt {x^{2}+c_{1}}\right ) x \\ y \left (x \right ) &= \left (-x +\sqrt {x^{2}+c_{1}}\right ) x \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.493 (sec). Leaf size: 67

DSolve[(y[x]^2)-(x*y[x]+x^3)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -x^2 \left (1+\sqrt {\frac {1}{x^3}} \sqrt {x \left (x^2+c_1\right )}\right ) \\ y(x)\to x^2 \left (-1+\sqrt {\frac {1}{x^3}} \sqrt {x \left (x^2+c_1\right )}\right ) \\ y(x)\to 0 \\ \end{align*}