12.5.51 problem 50

Internal problem ID [1675]
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 : 50
Date solved : Monday, January 27, 2025 at 05:24:56 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 50

dsolve(2*x*(y(x)+2*sqrt(x))*diff(y(x),x)=(y(x)+sqrt(x))^2,y(x), singsol=all)
 

\begin{align*} y &= \frac {-2 x +\sqrt {x^{2} \left (\ln \left (x \right )-c_1 +4\right )}}{\sqrt {x}} \\ y &= -\frac {2 x +\sqrt {x^{2} \left (\ln \left (x \right )-c_1 +4\right )}}{\sqrt {x}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.584 (sec). Leaf size: 68

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

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