Internal problem ID [2265]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 25, page 112
Problem number: 16.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }-x y^{\prime }+4 y=\sin \left (\ln \left (x \right )\right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 164
dsolve(x^3*diff(y(x),x$3)-2*x^2*diff(y(x),x$2)-x*diff(y(x),x)+4*y(x)=sin(ln(x)),y(x), singsol=all)
\[ y = -\frac {\left (119 i x^{2 i} x^{-\frac {\sqrt {5}}{2}+\frac {1}{2}} x^{\frac {\sqrt {5}}{2}+\frac {1}{2}}-20 i x^{2 i} x +17 x^{2 i} x^{-\frac {\sqrt {5}}{2}+\frac {1}{2}} x^{\frac {\sqrt {5}}{2}+\frac {1}{2}}-119 i x^{-\frac {\sqrt {5}}{2}+\frac {1}{2}} x^{\frac {\sqrt {5}}{2}+\frac {1}{2}}+5 x^{2 i} x +20 i x +17 x^{-\frac {\sqrt {5}}{2}+\frac {1}{2}} x^{\frac {\sqrt {5}}{2}+\frac {1}{2}}+5 x \right ) x^{-i}}{1870 x}+c_{1} x^{4}+c_{2} x^{-\frac {\sqrt {5}}{2}+\frac {1}{2}}+c_{3} x^{\frac {\sqrt {5}}{2}+\frac {1}{2}} \]
✓ Solution by Mathematica
Time used: 0.212 (sec). Leaf size: 60
DSolve[x^3*y'''[x]-2*x^2*y''[x]-x*y'[x]+4*y[x]==Sin[Log[x]],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 x^{\frac {1}{2} \left (1+\sqrt {5}\right )}+c_1 x^{\frac {1}{2}-\frac {\sqrt {5}}{2}}+c_3 x^4+\frac {9}{85} \sin (\log (x))-\frac {2}{85} \cos (\log (x)) \]