60.1.26 problem 26

Internal problem ID [10040]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 26
Date solved : Monday, January 27, 2025 at 06:19:14 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }-\left (A y-a \right ) \left (B y-b \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 45

dsolve(diff(y(x),x) - (A*y(x) - a)*(B*y(x) - b)=0,y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{\left (x +c_{1} \right ) \left (A b -a B \right )} a -b}{A \,{\mathrm e}^{\left (x +c_{1} \right ) \left (A b -a B \right )}-B} \]

✓ Solution by Mathematica

Time used: 0.382 (sec). Leaf size: 56

DSolve[D[y[x],x] - (A*y[x] - a)*(B*y[x] - b)==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(a-A K[1]) (b-B K[1])}dK[1]\&\right ][x+c_1] \\ y(x)\to \frac {a}{A} \\ y(x)\to \frac {b}{B} \\ \end{align*}