Internal problem ID [2541]
Book: Elementary Differential equations, Chaundy, 1969
Section: Exercises 3, page 60
Problem number: 5(c).
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 )}\, \left (2 y^{\prime }-3\right )+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 63
dsolve(sqrt((x+a)*(x+b))*(2*diff(y(x),x)-3)+y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {2 \left (\int \frac {3 \sqrt {2 a +2 b +4 x +4 \sqrt {\left (x +a \right ) \left (x +b \right )}}}{4}d x \right )+2 c_{1}}{\sqrt {2 a +2 b +4 x +4 \sqrt {x^{2}+\left (a +b \right ) x +a b}}} \]
✓ Solution by Mathematica
Time used: 0.468 (sec). Leaf size: 115
DSolve[Sqrt[(x+a)*(x+b)]*(2*y'[x]-3)+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \exp \left (-\frac {\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 {3}{2} \exp \left (\frac {\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 )dK[1]+c_1\right ) \\ \end{align*}