Internal problem ID [5797]
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]
\[ \boxed {2 y^{\prime }-4 \sqrt {y}=-x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 100
dsolve(2*diff(y(x),x)+x=4*sqrt(y(x)),y(x), singsol=all)
\[ \frac {\left (-x^{2}+4 y \left (x \right )\right ) \ln \left (\frac {x^{2}-4 y \left (x \right )}{x^{2}}\right )+2 i \left (x^{2}-4 y \left (x \right )\right ) \arctan \left (2 \sqrt {-\frac {y \left (x \right )}{x^{2}}}\right )-4 i \sqrt {-\frac {y \left (x \right )}{x^{2}}}\, x^{2}+4 \left (-c_{1} +2 \ln \left (x \right )\right ) y \left (x \right )+x^{2} \left (c_{1} -2 \ln \left (x \right )-2\right )}{x^{2}-4 y \left (x \right )} = 0 \]
✓ Solution by Mathematica
Time used: 0.104 (sec). Leaf size: 49
DSolve[2*y'[x]+x==4*Sqrt[y[x]],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [4 \left (\frac {4}{4 \sqrt {\frac {y(x)}{x^2}}+2}+2 \log \left (4 \sqrt {\frac {y(x)}{x^2}}+2\right )\right )=-8 \log (x)+c_1,y(x)\right ] \]