Internal problem ID [5044]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems.
page 12
Problem number: 45.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Chini]
Solve \begin {gather*} \boxed {2 y^{\prime }+x -4 \sqrt {y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 111
dsolve(2*diff(y(x),x)+x=4*sqrt(y(x)),y(x), singsol=all)
\[ -\frac {4 i x^{2} \sqrt {-\frac {y \relax (x )}{x^{2}}}-2 i \arctan \left (2 \sqrt {-\frac {y \relax (x )}{x^{2}}}\right ) x^{2}+8 i \arctan \left (2 \sqrt {-\frac {y \relax (x )}{x^{2}}}\right ) y \relax (x )+\ln \left (\frac {x^{2}-4 y \relax (x )}{x^{2}}\right ) x^{2}-4 \ln \left (\frac {x^{2}-4 y \relax (x )}{x^{2}}\right ) y \relax (x )+2 x^{2}}{x^{2}-4 y \relax (x )}-2 \ln \relax (x )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.101 (sec). Leaf size: 49
DSolve[2*y'[x]+x==4*Sqrt[y[x]],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [4 \left (\frac {4}{4 \sqrt {\frac {y(x)}{x^2}}+2}+2 \log \left (4 \sqrt {\frac {y(x)}{x^2}}+2\right )\right )=-8 \log (x)+c_1,y(x)\right ] \]