Internal problem ID [8986]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1407.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\left (\frac {\left (1-\mathit {al1} -\mathit {bl1} \right ) \mathit {b1}}{x \mathit {b1} -\mathit {a1}}+\frac {\left (1-\mathit {al2} -\mathit {bl2} \right ) \mathit {b2}}{x \mathit {b2} -\mathit {a2}}+\frac {\left (1-\mathit {al3} -\mathit {bl3} \right ) \mathit {b3}}{x \mathit {b3} -\mathit {a3}}\right ) y^{\prime }+\frac {\left (\frac {\mathit {al1} \mathit {bl1} \left (\mathit {a1} \mathit {b2} -\mathit {a2} \mathit {b1} \right ) \left (-\mathit {a1} \mathit {b3} +\mathit {a3} \mathit {b1} \right )}{x \mathit {b1} -\mathit {a1}}+\frac {\mathit {al2} \mathit {bl2} \left (\mathit {a2} \mathit {b3} -\mathit {a3} \mathit {b2} \right ) \left (\mathit {a1} \mathit {b2} -\mathit {a2} \mathit {b1} \right )}{x \mathit {b2} -\mathit {a2}}+\frac {\mathit {al3} \mathit {bl3} \left (-\mathit {a1} \mathit {b3} +\mathit {a3} \mathit {b1} \right ) \left (\mathit {a2} \mathit {b3} -\mathit {a3} \mathit {b2} \right )}{x \mathit {b3} -\mathit {a3}}\right ) y}{\left (x \mathit {b1} -\mathit {a1} \right ) \left (x \mathit {b2} -\mathit {a2} \right ) \left (x \mathit {b3} -\mathit {a3} \right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 1.281 (sec). Leaf size: 3211
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: 79.49 (sec). Leaf size: 1270
DSolve[y''[x] == -((((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))*y'[x],y[x],x,IncludeSingularSolutions -> True]
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