Internal problem ID [7639]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 58.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _Chini]
Solve \begin {gather*} \boxed {y^{\prime }-a \sqrt {y}-b x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 68
dsolve(diff(y(x),x) - a*sqrt(y(x)) - b*x=0,y(x), singsol=all)
\[ -\frac {\ln \left (\sqrt {y \relax (x )}\, a x +b \,x^{2}-2 y \relax (x )\right )}{2}+\frac {a \sqrt {y \relax (x )}\, \arctanh \left (\frac {a \sqrt {y \relax (x )}+2 b x}{\sqrt {y \relax (x ) \left (a^{2}+8 b \right )}}\right )}{\sqrt {y \relax (x ) \left (a^{2}+8 b \right )}}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.242 (sec). Leaf size: 119
DSolve[y'[x] - a*Sqrt[y[x]] - b*x==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {a^2 \left (-\log \left (a^2 \left (\sqrt {\frac {a^2 y(x)}{b^2 x^2}}+1\right )-\frac {2 a^2 y(x)}{b x^2}\right )-\frac {2 a \tanh ^{-1}\left (\frac {a^2-4 b \sqrt {\frac {a^2 y(x)}{b^2 x^2}}}{a \sqrt {a^2+8 b}}\right )}{\sqrt {a^2+8 b}}\right )}{2 b}=\frac {a^2 \log (x)}{b}+c_1,y(x)\right ] \]