12.3.28 problem 36

Internal problem ID [1605]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. separable equations. Section 2.2 Page 52
Problem number : 36
Date solved : Monday, January 27, 2025 at 05:13:38 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} x y^{\prime }-2 y&=\frac {x^{6}}{y+x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 41

dsolve(x*diff(y(x),x)-2*y(x)=x^6/(y(x)+x^2),y(x), singsol=all)
 

\begin{align*} y &= \left (-1-\sqrt {x^{2}-2 c_1 +1}\right ) x^{2} \\ y &= \left (-1+\sqrt {x^{2}-2 c_1 +1}\right ) x^{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.639 (sec). Leaf size: 70

DSolve[x*D[y[x],x]-2*y[x]==x^6/(y[x]+x^2),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -x^2 \left (1+\sqrt {\frac {1}{x^5}} x^2 \sqrt {x \left (x^2+1+c_1\right )}\right ) \\ y(x)\to -x^2+\sqrt {\frac {1}{x^5}} x^4 \sqrt {x \left (x^2+1+c_1\right )} \\ \end{align*}