12.5.4 problem Example 3(b)

Internal problem ID [1628]
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 : Example 3(b)
Date solved : Monday, January 27, 2025 at 05:15:11 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

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

With initial conditions

\begin{align*} y \left (1\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.043 (sec). Leaf size: 19

dsolve([x^2*diff(y(x),x)=y(x)^2+x*y(x)-x^2,y(1) = 2],y(x), singsol=all)
 

\[ y = -\frac {x \left (x^{2}+3\right )}{x^{2}-3} \]

✓ Solution by Mathematica

Time used: 0.480 (sec). Leaf size: 20

DSolve[{x^2*D[y[x],x]==y[x]^2+x*y[x]-x^2,y[1]==2},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {x \left (x^2+3\right )}{x^2-3} \]