Internal problem ID [2264]
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.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {x^{4} y^{\prime \prime \prime \prime }+7 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }-6 x y^{\prime }-6 y=\cos \left (\ln \left (x \right )\right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 289
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)
\[ y \left (x \right ) = \frac {\left (\left (\left (-66-132 i+\left (-33+99 i\right ) \sqrt {2}\right ) x^{1-i}+\left (-66+132 i+\left (33+99 i\right ) \sqrt {2}\right ) x^{1+i}-360 i \sqrt {2}\, c_{2} x^{3}+240 c_{2} x^{3}-440 c_{1} \right ) x^{-i \sqrt {2}}+\left (\left (-66-132 i+\left (33-99 i\right ) \sqrt {2}\right ) x^{1-i}+\left (-66+132 i+\left (-33-99 i\right ) \sqrt {2}\right ) x^{1+i}+360 i \sqrt {2}\, c_{2} x^{3}+240 c_{2} x^{3}-440 c_{1} \right ) x^{i \sqrt {2}}+5280 c_{3} \right ) \cos \left (\sqrt {2}\, \ln \left (x \right )\right )+240 \sin \left (\sqrt {2}\, \ln \left (x \right )\right ) \left (\left (\left (\frac {11}{20}-\frac {11 i}{40}+\left (-\frac {33}{80}-\frac {11 i}{80}\right ) \sqrt {2}\right ) x^{1-i}+\left (-\frac {11}{20}-\frac {11 i}{40}+\left (-\frac {33}{80}+\frac {11 i}{80}\right ) \sqrt {2}\right ) x^{1+i}+i x^{3} c_{2} +\frac {3 \sqrt {2}\, c_{2} x^{3}}{2}-\frac {11 i c_{1}}{6}\right ) x^{-i \sqrt {2}}+\left (\left (-\frac {11}{20}+\frac {11 i}{40}+\left (-\frac {33}{80}-\frac {11 i}{80}\right ) \sqrt {2}\right ) x^{1-i}+\left (\frac {11}{20}+\frac {11 i}{40}+\left (-\frac {33}{80}+\frac {11 i}{80}\right ) \sqrt {2}\right ) x^{1+i}-i x^{3} c_{2} +\frac {3 \sqrt {2}\, c_{2} x^{3}}{2}+\frac {11 i c_{1}}{6}\right ) x^{i \sqrt {2}}+22 c_{4} \right )}{5280 x} \]
✓ Solution by Mathematica
Time used: 0.318 (sec). Leaf size: 62
DSolve[x^4*y''''[x]+7*x^3*y'''[x]+9*x^2*y''[x]-6*x*y'[x]-6*y[x]==Cos[Log[x]],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_4 x^2+\frac {c_3}{x}-\frac {1}{10} \sin (\log (x))-\frac {1}{20} \cos (\log (x))+\frac {c_2 \cos \left (\sqrt {2} \log (x)\right )}{x}+\frac {c_1 \sin \left (\sqrt {2} \log (x)\right )}{x} \]