Internal problem ID [2848]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 4
Problem number: 99.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-a -b y-\sqrt {\mathit {A0} +\mathit {B0} y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 27
dsolve(diff(y(x),x) = a+b*y(x)+sqrt(A0+B0*y(x)),y(x), singsol=all)
\[ x -\left (\int _{}^{y \relax (x )}\frac {1}{a +b \textit {\_a} +\sqrt {\mathit {B0} \textit {\_a} +\mathit {A0}}}d \textit {\_a} \right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.701 (sec). Leaf size: 172
DSolve[y'[x]==a+b y[x]+Sqrt[A0+B0 y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [\frac {\log \left (-\text {B0} \left (\sqrt {\text {$\#$1} \text {B0}+\text {A0}}+\text {$\#$1} b+a\right )\right )-\frac {2 \text {B0} \text {ArcTan}\left (\frac {2 b \sqrt {\text {$\#$1} \text {B0}+\text {A0}}+\text {B0}}{\sqrt {\text {B0} (4 a b-\text {B0})-4 \text {A0} b^2}}\right )}{\sqrt {\text {B0} (4 a b-\text {B0})-4 \text {A0} b^2}}}{b}\&\right ][x+c_1] \\ y(x)\to -\frac {\sqrt {-4 a b \text {B0}+4 \text {A0} b^2+\text {B0}^2}+2 a b-\text {B0}}{2 b^2} \\ y(x)\to \frac {\sqrt {-4 a b \text {B0}+4 \text {A0} b^2+\text {B0}^2}-2 a b+\text {B0}}{2 b^2} \\ \end{align*}