12.5.7 problem 3

Internal problem ID [1631]
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 : 3
Date solved : Monday, January 27, 2025 at 05:15:17 AM
CAS classification : [_Bernoulli]

\begin{align*} x^{2} y^{\prime }+2 y&=2 \,{\mathrm e}^{\frac {1}{x}} \sqrt {y} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 26

dsolve(x^2*diff(y(x),x)+2*y(x)=2*exp(1/x)*y(x)^(1/2),y(x), singsol=all)
 

\[ \frac {-c_1 x \,{\mathrm e}^{\frac {1}{x}}+x \sqrt {y}+{\mathrm e}^{\frac {1}{x}}}{x} = 0 \]

✓ Solution by Mathematica

Time used: 0.171 (sec). Leaf size: 39

DSolve[D[y[x],x]+2*y[x]==2*Exp[1/x]*y[x]^(1/2),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} e^{-2 x} \left (\int _1^x2 e^{K[1]+\frac {1}{K[1]}}dK[1]+2 c_1\right ){}^2 \]