Internal problem ID [2542]
Book: Elementary Differential equations, Chaundy, 1969
Section: Exercises 3, page 60
Problem number: 5(d).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\sqrt {\left (x +a \right ) \left (x +b \right )}\, y^{\prime }+y-\sqrt {x +a}+\sqrt {x +b}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 103
dsolve(sqrt((x+a)*(x+b))*diff(y(x),x)+y(x)=sqrt(x+a)-sqrt(x+b),y(x), singsol=all)
\[ y \relax (x ) = \frac {\frac {2 \left (x +a \right )^{\frac {3}{2}}}{3}-\frac {2 \left (x +b \right )^{\frac {3}{2}}}{3}+\frac {\sqrt {x +a}\, \left (x +b \right ) \left (2 x -b +3 a \right )}{3 \sqrt {\left (x +a \right ) \left (x +b \right )}}-\frac {\sqrt {x +b}\, \left (x +a \right ) \left (2 x -a +3 b \right )}{3 \sqrt {\left (x +a \right ) \left (x +b \right )}}+c_{1}}{\frac {a}{2}+\frac {b}{2}+x +\sqrt {x^{2}+\left (a +b \right ) x +a b}} \]
✓ Solution by Mathematica
Time used: 1.546 (sec). Leaf size: 145
DSolve[Sqrt[(x+a)*(x+b)]*y'[x]+y[x]==Sqrt[x+a]-Sqrt[x+b],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \exp \left (-\frac {2 \sqrt {a+x} \sqrt {b+x} \tanh ^{-1}\left (\frac {\sqrt {b+x}}{\sqrt {a+x}}\right )}{\sqrt {(a+x) (b+x)}}\right ) \left (\int _1^x\frac {\exp \left (\frac {2 \tanh ^{-1}\left (\frac {\sqrt {b+K[1]}}{\sqrt {a+K[1]}}\right ) \sqrt {a+K[1]} \sqrt {b+K[1]}}{\sqrt {(a+K[1]) (b+K[1])}}\right ) \left (\sqrt {a+K[1]}-\sqrt {b+K[1]}\right )}{\sqrt {(a+K[1]) (b+K[1])}}dK[1]+c_1\right ) \\ \end{align*}