Internal problem ID [13478]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 24. Variation of parameters. Additional exercises page 444
Problem number: 24.4 (d).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-9 y^{\prime } x +9 y=12 x \sin \left (x^{2}\right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 72
dsolve(x^4*diff(y(x),x$4)+6*x^3*diff(y(x),x$3)-3*x^2*diff(y(x),x$2)-9*x*diff(y(x),x)+9*y(x)=12*x*sin(x^2),y(x), singsol=all)
\[ y = -\frac {-2 \,\operatorname {Ci}\left (x^{2}\right ) x^{6}+2 \sin \left (x^{2}\right ) x^{4}+6 \,\operatorname {Si}\left (x^{2}\right ) x^{4}+4 x^{2} \cos \left (x^{2}\right )-c_{1} x^{2}+2 \sin \left (x^{2}\right )}{16 x^{3}}+c_{2} x +\frac {c_{3}}{x^{3}}+c_{4} x^{3} \]
✓ Solution by Mathematica
Time used: 0.032 (sec). Leaf size: 79
DSolve[x^4*y''''[x]+6*x^3*y'''[x]-3*x^2*y''[x]-9*x*y'[x]+9*y[x]==12*x*Sin[x^2],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^6 \operatorname {CosIntegral}\left (x^2\right )-3 x^4 \text {Si}\left (x^2\right )+8 c_4 x^6+8 c_3 x^4-\sin \left (x^2\right )-2 x^2 \cos \left (x^2\right )+8 c_2 x^2-x^4 \sin \left (x^2\right )+8 c_1}{8 x^3} \]