12.5.38 problem 35(a)

Internal problem ID [1662]
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 : 35(a)
Date solved : Monday, January 27, 2025 at 05:21:58 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

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

With initial conditions

\begin{align*} y \left (-1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.358 (sec). Leaf size: 21

dsolve([x^2*diff(y(x),x)=y(x)^2+x*y(x)-4*x^2,y(-1) = 0],y(x), singsol=all)
 

\[ y = \frac {-2 x^{5}+2 x}{x^{4}+1} \]

✓ Solution by Mathematica

Time used: 2.110 (sec). Leaf size: 20

DSolve[{x^2*D[y[x],x]==y[x]^2+x*y[x]-4*x^2,y[-1]==0},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {2 x \left (x^4-1\right )}{x^4+1} \]