15.16.15 problem 15

Internal problem ID [3235]
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 : 15
Date solved : Monday, January 27, 2025 at 07:27:13 AM
CAS classification : [[_high_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+7 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }-6 x y^{\prime }-6 y&=\cos \left (\ln \left (x \right )\right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 49

dsolve(x^4*diff(y(x),x$4)+7*x^3*diff(y(x),x$3)+9*x^2*diff(y(x),x$2)-6*x*diff(y(x),x)-6*y(x)=cos(ln(x)),y(x), singsol=all)
 

\[ y = \frac {1320 \cos \left (\sqrt {2}\, \ln \left (x \right )\right ) c_3 +1320 \sin \left (\sqrt {2}\, \ln \left (x \right )\right ) c_4 +\left (-33-66 i\right ) x^{1-i}+\left (-33+66 i\right ) x^{1+i}+120 c_2 \,x^{3}-220 c_{1}}{1320 x} \]

✓ Solution by Mathematica

Time used: 0.345 (sec). Leaf size: 62

DSolve[x^4*D[y[x],{x,4}]+7*x^3*D[y[x],{x,3}]+9*x^2*D[y[x],{x,2}]-6*x*D[y[x],x]-6*y[x]==Cos[Log[x]],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_4 x^2+\frac {c_3}{x}-\frac {1}{10} \sin (\log (x))-\frac {1}{20} \cos (\log (x))+\frac {c_2 \cos \left (\sqrt {2} \log (x)\right )}{x}+\frac {c_1 \sin \left (\sqrt {2} \log (x)\right )}{x} \]