12.4.12 problem 12

Internal problem ID [1619]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Existence and Uniqueness of Solutions of Nonlinear Equations. Section 2.3 Page 60
Problem number : 12
Date solved : Monday, January 27, 2025 at 05:14:11 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 42

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

\[ x -2 \sqrt {x +y}-\ln \left (-1+\sqrt {x +y}\right )+\ln \left (1+\sqrt {x +y}\right )+\ln \left (x +y-1\right )-c_1 = 0 \]

✓ Solution by Mathematica

Time used: 7.968 (sec). Leaf size: 59

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

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