12.5.29 problem 26

Internal problem ID [1653]
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 : 26
Date solved : Monday, January 27, 2025 at 05:18:01 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.032 (sec). Leaf size: 21

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

\[ y = \frac {-4 x^{2}+3 x}{2 x -3} \]

✓ Solution by Mathematica

Time used: 0.440 (sec). Leaf size: 20

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

\[ y(x)\to -\frac {x (4 x-3)}{2 x-3} \]