24.1.22 problem 5(c)

Internal problem ID [4211]
Book : Elementary Differential equations, Chaundy, 1969
Section : Exercises 3, page 60
Problem number : 5(c)
Date solved : Monday, January 27, 2025 at 08:42:24 AM
CAS classification : [_linear]

\begin{align*} \sqrt {\left (x +a \right ) \left (x +b \right )}\, \left (2 y^{\prime }-3\right )+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 60

dsolve(sqrt((x+a)*(x+b))*(2*diff(y(x),x)-3)+y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {3 \left (\int \sqrt {2 a +2 b +4 x +4 \sqrt {\left (x +a \right ) \left (x +b \right )}}d x \right )+4 c_{1}}{2 \sqrt {2 a +2 b +4 x +4 \sqrt {\left (x +a \right ) \left (x +b \right )}}} \]

✓ Solution by Mathematica

Time used: 0.391 (sec). Leaf size: 115

DSolve[Sqrt[(x+a)*(x+b)]*(2*D[y[x],x]-3)+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \exp \left (-\frac {\sqrt {a+x} \sqrt {b+x} \text {arctanh}\left (\frac {\sqrt {b+x}}{\sqrt {a+x}}\right )}{\sqrt {(a+x) (b+x)}}\right ) \left (\int _1^x\frac {3}{2} \exp \left (\frac {\text {arctanh}\left (\frac {\sqrt {b+K[1]}}{\sqrt {a+K[1]}}\right ) \sqrt {a+K[1]} \sqrt {b+K[1]}}{\sqrt {(a+K[1]) (b+K[1])}}\right )dK[1]+c_1\right ) \]