12.5.28 problem 25

Internal problem ID [1652]
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 : 25
Date solved : Monday, January 27, 2025 at 05:17:57 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

\begin{align*} y^{\prime }&=\frac {y^{2}-3 y x -5 x^{2}}{x^{2}} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.331 (sec). Leaf size: 23

dsolve([diff(y(x),x)=(y(x)^2-3*x*y(x)-5*x^2)/x^2,y(1) = 1],y(x), singsol=all)
 

\[ y = \frac {-2 x^{7}+5 x}{2 x^{6}+1} \]

✓ Solution by Mathematica

Time used: 1.890 (sec). Leaf size: 24

DSolve[{D[y[x],x]==(y[x]^2-3*x*y[x]-5*x^2)/x^2,y[1]==1},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {5 x-2 x^7}{2 x^6+1} \]