Internal problem ID [2849]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 4
Problem number: 100.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _Chini]
Solve \begin {gather*} \boxed {y^{\prime }-a x -\sqrt {y}\, b=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 68
dsolve(diff(y(x),x) = a*x+b*sqrt(y(x)),y(x), singsol=all)
\[ -\frac {\ln \left (\sqrt {y \relax (x )}\, b x +a \,x^{2}-2 y \relax (x )\right )}{2}+\frac {b \sqrt {y \relax (x )}\, \arctanh \left (\frac {b \sqrt {y \relax (x )}+2 a x}{\sqrt {y \relax (x ) \left (b^{2}+8 a \right )}}\right )}{\sqrt {y \relax (x ) \left (b^{2}+8 a \right )}}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.256 (sec). Leaf size: 119
DSolve[y'[x]==a x+b Sqrt[y[x]],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {b^2 \left (-\log \left (b^2 \left (\sqrt {\frac {b^2 y(x)}{a^2 x^2}}+1\right )-\frac {2 b^2 y(x)}{a x^2}\right )-\frac {2 b \tanh ^{-1}\left (\frac {b^2-4 a \sqrt {\frac {b^2 y(x)}{a^2 x^2}}}{b \sqrt {8 a+b^2}}\right )}{\sqrt {8 a+b^2}}\right )}{2 a}=\frac {b^2 \log (x)}{a}+c_1,y(x)\right ] \]