15.16.16 problem 16

Internal problem ID [3236]
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
Date solved : Monday, January 27, 2025 at 07:27:15 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }-x y^{\prime }+4 y&=\sin \left (\ln \left (x \right )\right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 42

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)
 

\[ y = c_2 \,x^{\frac {1}{2}-\frac {\sqrt {5}}{2}}+c_3 \,x^{\frac {1}{2}+\frac {\sqrt {5}}{2}}+\left (-\frac {1}{85}+\frac {9 i}{170}\right ) x^{-i}+\left (-\frac {1}{85}-\frac {9 i}{170}\right ) x^{i}+c_{1} x^{4} \]

✓ Solution by Mathematica

Time used: 0.234 (sec). Leaf size: 60

DSolve[x^3*D[y[x],{x,3}]-2*x^2*D[y[x],{x,2}]-x*D[y[x],x]+4*y[x]==Sin[Log[x]],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 x^{\frac {1}{2} \left (1+\sqrt {5}\right )}+c_1 x^{\frac {1}{2}-\frac {\sqrt {5}}{2}}+c_3 x^4+\frac {9}{85} \sin (\log (x))-\frac {2}{85} \cos (\log (x)) \]