60.3.401 problem 1407

Internal problem ID [11411]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1407
Date solved : Tuesday, January 28, 2025 at 06:05:07 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }&=-\left (\frac {\left (1-\operatorname {al1} -\operatorname {bl1} \right ) \operatorname {b1}}{\operatorname {b1} x -\operatorname {a1}}+\frac {\left (1-\operatorname {al2} -\operatorname {bl2} \right ) \operatorname {b2}}{\operatorname {b2} x -\operatorname {a2}}+\frac {\left (1-\operatorname {al3} -\operatorname {bl3} \right ) \operatorname {b3}}{\operatorname {b3} x -\operatorname {a3}}\right ) y^{\prime }-\frac {\left (\frac {\operatorname {al1} \operatorname {bl1} \left (\operatorname {a1} \operatorname {b2} -\operatorname {a2} \operatorname {b1} \right ) \left (-\operatorname {a1} \operatorname {b3} +\operatorname {a3} \operatorname {b1} \right )}{\operatorname {b1} x -\operatorname {a1}}+\frac {\operatorname {al2} \operatorname {bl2} \left (\operatorname {a2} \operatorname {b3} -\operatorname {a3} \operatorname {b2} \right ) \left (\operatorname {a1} \operatorname {b2} -\operatorname {a2} \operatorname {b1} \right )}{\operatorname {b2} x -\operatorname {a2}}+\frac {\operatorname {al3} \operatorname {bl3} \left (-\operatorname {a1} \operatorname {b3} +\operatorname {a3} \operatorname {b1} \right ) \left (\operatorname {a2} \operatorname {b3} -\operatorname {a3} \operatorname {b2} \right )}{\operatorname {b3} x -\operatorname {a3}}\right ) y}{\left (\operatorname {b1} x -\operatorname {a1} \right ) \left (\operatorname {b2} x -\operatorname {a2} \right ) \left (\operatorname {b3} x -\operatorname {a3} \right )} \end{align*}

✓ Solution by Maple

Time used: 7.205 (sec). Leaf size: 2220

dsolve(diff(diff(y(x),x),x) = -((1-al1-bl1)*b1/(b1*x-a1)+(1-al2-bl2)*b2/(b2*x-a2)+(1-al3-bl3)*b3/(b3*x-a3))*diff(y(x),x)-1/(b1*x-a1)/(b2*x-a2)/(b3*x-a3)*(al1*bl1*(a1*b2-a2*b1)*(-a1*b3+a3*b1)/(b1*x-a1)+al2*bl2*(a2*b3-a3*b2)*(a1*b2-a2*b1)/(b2*x-a2)+al3*bl3*(-a1*b3+a3*b1)*(a2*b3-a3*b2)/(b3*x-a3))*y(x),y(x), singsol=all)
 

\[ \text {Expression too large to display} \]

✓ Solution by Mathematica

Time used: 140.502 (sec). Leaf size: 1290

DSolve[D[y[x],{x,2}] == -((((al1*(-(a2*b1) + a1*b2)*(a3*b1 - a1*b3)*bl1)/(-a1 + b1*x) + (al2*(-(a2*b1) + a1*b2)*(-(a3*b2) + a2*b3)*bl2)/(-a2 + b2*x) + (al3*(a3*b1 - a1*b3)*(-(a3*b2) + a2*b3)*bl3)/(-a3 + b3*x))*y[x])/((-a1 + b1*x)*(-a2 + b2*x)*(-a3 + b3*x))) - ((b1*(1 - al1 - bl1))/(-a1 + b1*x) + (b2*(1 - al2 - bl2))/(-a2 + b2*x) + (b3*(1 - al3 - bl3))/(-a3 + b3*x))*D[y[x],x],y[x],x,IncludeSingularSolutions -> True]
 

Too large to display